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A Novel, Game Theory-Based Approach to Better Understand Incentives and Stability in Clusters Endre Gedai, László Á. Kóczy, Zita Zombori László Á. Kóczy Gerd Meier zu Köcker, Institute for Innovation and Technology, iit (Berlin) Thomas A. Christensen Danish Ministry for Science, Technology and Innovation, DASTI (Copenhagen) Copenhagen, Berlin 2012 Countries all over the world look for ways to increase their competitiveness. The contribution of cooperating com- panies in the form of clusters is rather substantial and therefore, for example, the European Union and its member states have long been supporting these cooperative efforts. This support may take the form of a more entrepre- neur-friendly legal environment, initiate cooperation, but it may also mean non-returnable financial contribution. This paper does not want to discuss the optimal channels to support clusters, and in particular it does not want to study the ways financial contributions are distributed among clusters. Rather, the contribution is an entirely novel way to look at the forces that keep some clusters on track while destruct others. Longstanding cooperation between companies forms a special complex process hierarchy in clusters. The main businesses of the cluster is driven by the actors' interests in staying competitive, improving competitiveness and obtaining high profits both as a cluster, but especially as an individual company. Cooperation and the actors' selfish interests should be kept in balance or else the success of the cluster is in jeopardy and its actors can lose both joint and individual profits. Organic relationships and cooperation among companies or a favourable business environment is, by no means a guarantee for a working and successful cluster. Clusters operating at industrial concentration points, having a critical mass, supporting environment, and a successful cluster manager may nevertheless lack success. On the other hand other clusters operating in suboptimal circumstances in theory, flourish and produce a high extra profit in practice. This puzzle cries for new models, new approaches for a better understanding of the opportunities and decisions that drive the clusters and their actors. This paper introduces an entirely novel way to study clusters by looking at the selfish, profit-seeking interests of the entrepreneurs, the actors of clusters. The approach, using game theory provides an exact, mathematical framework to study the conflict between the fruitful cooperation represented by the cluster and the selfish ways of the actors to follow their own – possibly short term – interests. The game theoretic approach makes it possible to identify not only good or bad clusters, provide recipes for solutions in some of the bad clusters, but also to define golden rules that do not only facilitate the evaluation of existing clusters, but help future cluster managers to create better, more stable clusters.
Table of contents
Executive summary . 3
Clusters and game theory . 7
I.1 Cooperation of the companies . 7 I.4 Cluster policies and cluster-based economic development . 9 I.5 The cluster management organisation . 10 I.6 Key elements – Trust and social capital . 10 theory . 13
II.1 Non-cooperative II.2 Cooperative III Cluster
games . 21
III.1 Where are the coalitions in clusters? . 21 III.2 About translating clusters into games . 23 III.3 The bases of decision making: Do actors like profit? . 24 III.4 Cluster code – structure: Do actors think about present and future alternatives? . 26 IV Setting the golden rules . 27
IV.1 Joining a cluster: Do actors look for profit? . 27 IV.2 Cluster code: How to keep all cluster actors happy at the same time? . 29 IV.3. Social networks: How do projects form? . 30 V Hypothesis
testing. 31
V.1 Fundamentals of decision making . 31 V.2 Profitability V.3 Networks . 32 V.4 Conclusions on the data . 32 VI Conclusion . 33
VII Bibliography . 34
VIII Authors . 37
Zita Zombori . 37 László Á. Kóczy . 37 Clusters and game theory Clusters and game theory
Today the formation of clusters – the collaboration of compa- Without being absorbed in a form and content analysis of the nies with each other and with the research sector – is seen as a companies and the institutions in contact with them, it is nec- possibility to renew the economy and the society. Clusters have essary to mention the classification made by Jacobs and De been proven as a very promising tool to strengthen the com- Man. They define clusters in a three-fold manner as either be- petitiveness of companies all over the world. Competitiveness ing regionally located, as possessing a vertical production and significantly increases among cluster actors which are closely supply chain process or third, as businesses that are related by located within a region and willing to do joint research, devel- some form of narrowly-focused specialization. Links the cluster opment as well as to jointly create innovations. Clusters offer definitions to the development of industrial policy in The Neth- a favourable and dynamic business environment (ecosystem) erlands, and from the discussion compiles a menu of possible where innovative companies can flourish by interacting with policies and strategies that can be utilized by both industry and different innovation actors and across sectoral boundaries. government for the furtherance of industrial policy. (Jacobs & Recognizing these positive roles the development of clusters is actively supported by policy makers worldwide.
In conclusion our opinion is that longstanding coopera-
tion between companies forms a special process making
Cooperation of the companies
complex hierarchy which main business motives basi-
cally are driven by the ideas of staying alive and being
History proves that humanity is ready for cooperation and it competitive and strengthening this competitiveness as
needs cooperation. To put it simply, the modern enterprise is a well as maximizing the profit.
typical product of modern people's cooperation and the rela- tions between the enterprises and other organizations mean a The fact that the forms of companies' cooperation are
more advanced stage in the cooperation's hierarchy.
continuously developing and this cooperation has a spe-
cial evolution progress – the successful solutions will be
Alfred Marshall in his book – Principles of Economics (Marshall, commonly used and the less successful initiatives will
1890) – shed light on the positive effect of the concentration of die – is noteworthy as well.
specialized industries in a particular area. His concept was based on a pattern of organization that was I.2 Clusters
common in late nineteenth century Britain in which compa- nies concentrating on the manufacture of certain products Moving on to the particular subject of the concept paper, it were geographically clustered. Comments made by Marshall would be worth beginning with a definition which clarifies (1890, Book 4, Chapter 10) have been used by economists and the concept of cluster, with one, which is fully accepted by the economic geographers to discuss this phenomenon. The two community. In the literature many alternative, overlapping defi- dominant characteristics of a Marshallian industrial district are nitions are used, but there is no commonly accepted standard.
high degrees of vertical and horizontal specialisation and a very heavy reliance on market mechanism for exchange. Compa- Actually, the most known definition of cluster had become nies tend to be small and to focus on a single function in the public as a result of Michael E. Porter's work. In the 80's Porter production chain. Companies located in industrial districts are studied the factors of competitiveness. In connection with this highly competitive in the neoclassical sense, and in many cases research he clarified the positive effect on the competitiveness there is little product differentiation. The major advantages of of the regional and sectoral cooperation. Marshallian industrial districts arise from simple propinquity of companies, which allows easier recruitment of skilled labour The four factors of Porter's diamond model (company strategy, and rapid exchanges of commercial and technical information structure and rivalry; factor conditions; demand conditions; re- through informal channels. They illustrate competitive capital- lated and supporting industries) interact with each other to cre- ism at its most efficient, with transaction costs reduced to a ate conditions where innovation and improved competitiveness practical minimum; but they are feasible only when economic occur (Porter, 1990).
of scale are limited. (Wikipedia contributors, 2012; Zaratiegui, Based on this theory he introduced the concept of clusters: ‘A cluster is a geographically proximate group of interconnected companies and associated institutions in a particular field linked to realize higher profit than the total profit of the cluster
by commonalities and complementarities'. (Porter, 1998) actors. From the point of view of this concept paper it
is important to emphasize the observation implemented
Ketels (2004) draws four critical characteristics to our atten- in cluster definitions – cooperation and competition …
tion which is proximity, linkages, interactions and critical mass. both of them are characteristic for the cluster actors at
Understanding the importance of these four dimensions is the same time. But these two opposite attitudes should
much more important than defining specific benchmarks along be kept in balance among the cluster actors under any
them that a group of companies and institutions have to meet circumstances, otherwise either overweight could
to be called a cluster.
jeopar dize the success of the cluster.
‘The geographic scope of clusters can vary from a single city, state or region to a network of companies across state or even I.3 Cluster
country borders. There are various clustering forms that may ensue to optimise competitive advantage. Clustering can be Thanks to the work of Porter the positive impact of the clus- formal or informal, in the public or private sector; horizontal ters on the regional economy has become well known fast for or vertical; physical; and even sometimes virtual. In horizon- policy makers responsible for economic development. Taking tal clustering companies within the same industry sector are the advantage of this theory numerous economic strategies co-located in a particular geographic area and might share an have tried to get the benefit of the clusters' operation. The industrial or technological base, operate within a common mar- successful clusters can integrate the regional capacities with ket and use a common purchasing and/or distribution channel the special knowledge in their own value chain, which result (Michael, 2003). Vertical networks include horizontal cluster is an advantage that is hardly reached by others. The cluster participants as well as supply chain members such as suppli- itself is a favourable business environment for the SME's and ers, consumers and related services (Boekholt, 1997). Diago- it helps them (directly and indirectly as well), to easy connect nal clustering refers to the concentration of complementary or to the international economic trends. We can say that the clus- symbiotic activities, whereby each company adds value to the ters can be ready to be the heart not only of the well-working other.' (Braun, McRae-Williams, & Lowe, 2005) companies but of the regional development as well, thus if the cooperation-culture becomes general and is widely used in a The changes and the improvements of the cluster definition region, the development of a favourable business environment were induced by the realization of the influence of the organi- is only a child's play.
zations and institutions working in interaction in the market on the competitiveness and by the realization of the various forms Cluster development programmes based on economic politi- of cooperation of the cluster's framework. cal decisions proved that without (strong) base or a suitable approach there is no success, there are no successful initiatives. ‘Comparing the diversity of cluster definitions and approaches Examples for such failures are PANAC (Hungary) or IT Öresund throughout the literature, three common elements emerge: (Sweden and Denmark). geographic, economic integration, and social elements. In the literature, these elements are further divided into a number Nowadays it is a fact that the cluster itself can be a useful of dimensions (Bryant & Wells, 1998; Enright, 2000; Harrison, instrument in the economic development, but if the cluster 1992; Jacobs & De Man, 1996; Rosenfeld, 1997, 2001; Verbeek, funding itself has become the central goal for the cluster actors 1999), such as geographic localisation, vertical and horizontal and/or for the economic leaders, then the cluster can miss lose aggregation, innovation, critical mass, and social networks.' his basis basically needed to success. Clusters have to be con- (McRae-Williams, 2004) sidered as tools not as an objective.
We consider it important to mention that the essence
Regarding the cluster development our starting-point is
of clusters is based on empirical examinations and on a
that the clusters are ‘the product' of a long term evolu-
bottom up procedure. Funding and/or organizing a clus-
tionary process and at the same time they are a success-
ter is an organic instrument of the member companies to
ful instrument of the companies' struggle for survival
increase their competitiveness, which has a (back) posi-
and of obtaining (high) profit. One must therefore pay
tive effect on geographical and economic circumstances
attention to the cluster fundamentals, and the cluster's
of a cluster as well. Moreover cluster is an economic
motivations when evaluating a cluster's plan of opera-
device in the competitiveness development, with which
effective utilisation of a region's resources it is possible
Clusters and game theory Cluster policies and cluster-
teristics of these programs. Let us summarize the most impor- based economic development
Studies about the companies' cooperation have outlined the  ‘Common to all programs is their rationale of increas- role of geographical concentration of different activities and ing the competitiveness of the national economy through the conurbational benefits coming from it. From the point of the facilitation of collaboration between companies and view of the development of the cluster it is essential that poten- research stakeholders.' (Lämmer-Gamp, Meier zu Köcker, tial actors are present in ample number in geographical area, & Christensen, 2011, p 34) But there are different types of exceeding the critical mass. Therefore if statistical evidence the 16 cluster programs which serve different purposes. suggests that in a given geographical area the companies, The analysis of the objectives and strategies of the different which are willing to join a cluster, are present in higher than cluster program reveals the following main types of cluster the average density and their number, size and economic im- portance achieve the critical mass, an industrial cluster organi- I) Cluster programs that focus on regional economic develop- sation can be founded or the formation is already in progress. This method was adopted by Ketels & Sölvell (2004) in order to II) Cluster programs that focus on the development of national map the new member states' cluster organisations. III) Cluster programs that focus on the commercial exploitation In the recent years the European Union and some member of the R&D potential of a country's economy states have rightly committed considerable effort and resource  ‘Network programs to support the competitiveness of to the deeper understanding of clusters. Looking at the Euro- national industries.' (Lämmer-Gamp, Meier zu Köcker, & pean cluster landscape it becomes clear that some clusters are Christensen, 2011, pp 44–45) ‘Most programs support both more successful than others. Which clusters will likely be suc- the establishment of new cluster management organizations cessful? Which of these is it worth investing in? and the future development of already existing matured cluster management organizations. Only a few programs ‘In order to facilitate the discussion about cluster policy through concentrate either on the establishment of new cluster further insights into the characteristics of clusters and cluster organizations or the further development of already exist- policy intervention, the Danish Ministry of Research, Innova- ing matured cluster organizations.' (Lämmer-Gamp, Meier tion and Higher Education, supported by the German Federal zu Köcker, & Christensen, 2011, p 35) e. g. Competence Net- Ministry of Economics and Technology and its national cluster work Germany, Cluster Offensive Bayern, Norwegian Cen- program Initiative Kompetenznetze Deutschland, the Nordic tres of Expertise, Arena and Strategic Research Program for Council of Ministers and the Nordic Innovation Centre (NICe), Centres of Excellence and Research Clusters.
have initiated the project 'NGPExcellence – Cluster Excellence in  ‘Most programs do not have particular strategic objectives the Nordic Countries, Germany and Poland'. The overall objec- in terms of actors of clusters that are funded, restrictions on tive of this project is to contribute to the development of out- thematic areas and coverage of the most important business standing clusters through excellent management and excellent sectors.' (Lämmer-Gamp, Meier zu Köcker, & Christensen, cluster programs. … This project pays particular attention on 2011, p 37) Only Innovation Networks Denmark, the Nor- characteristics of cluster management organizations and their wegian Centres of Expertise Program and the Cluster Policy effects on cluster development. … As many cluster manage- Strategy of the Free and Hanseatic City of Hamburg concen- ment organizations are supported through national funding trate their efforts on the most important business sectors of programs the project also analyzed 16 cluster programs from the economy.
nine countries in a benchmarking exercise to facilitate a bet-  ‘Grant funding is the main instrument of nearly all cluster ter understanding of successful strategies and mutual learn- programs, while technical assistance for capacity develop- ing between the program owners. The project, … , addressed ment of cluster management organizations and its members two target groups: On the one hand, managers and staff of is applied by only half of the programs.' (Lämmer-Gamp, the cluster and network organizations from the participating Meier zu Köcker, & Christensen, 2011, p 39) ‘The most pro- countries, and on the other hand, program owners and policy grams co-fund initiatives to 50 or 75 per cent of the total makers responsible for national cluster and network programs project budget' (Lämmer-Gamp, Meier zu Köcker, & Chris- and policies.' (Lämmer-Gamp, Meier zu Köcker, & Christensen, tensen, 2011, p 41) and a number of cases there is no maxi- 2011, pp 10–11) mum funding period for a project or maximum amount of funding an applicant can apply for.
The examination of 16 different cluster programs in Europe gave the authors a unique opportunity to describe the charac- Looking at the European cluster policy landscape it becomes policies to newly emerging needs and challenges and exchange obvious that there are similarities but there is no common 'rec- knowledge and experience on the evaluation and impact ipe' for cluster policies, moreover there is no common 'recipe' assessment of cluster programmes.' (European Cluster Confer- for the success, just there are recommendations. The most im- ence, 2012, p 3).
portant ones were given by the European Cluster Policy Group issued in 2011. Building on them the INNO-Net project, the This concept paper does not deal directly with the ques-
TACTICS Reflection Group – the objective of which is to as- tion of the clusters' support, but it is even important
sist the TACTICS' partners to analyse, develop and propose from some point of view. We have to note though that
new cluster policy actions and methods of implementation in the subsidies of the clusters do deform or could deform
a number of predefined topics such as channelling RDI fund- the organic (economic) process of a cluster development.
ing through excellent clusters or user-driven excellent clusters, It can happen that the prime motivation of the cluster
among others – will issue in 2012 two handbooks on Cluster will be the extra profit getting with the help of subsi-
internationalisation and Cluster marketing & branding. dies or simply the subsidies will become a real part of
the profit. Therefore the cluster actors will get a false
Is it worth supporting clusters and if yes, how? – such ques- understanding of the cluster's operation and about its
tions raise a heated debate. As we mentioned before, different outcome. In any case – we should take these facts into
solutions are adopted. Which one of these is the best? Should account at the evaluation of a cluster's operation.
we give alternative possibilities for the subsidies for the cluster managers or for the cluster organizations or for the common cluster actors' projects or just for developing a favourable busi- The cluster management
ness environment? The success of the cluster development poli- cies can be measured only after years. And the next question this entails: How is it appropriate to measure the effects and The cluster management is the result of the conscious clus- impacts of clusters? The evaluation targets could be the target ter development whose task is among others to stimulate the policy or the cluster program or the cluster organization itself organic development of the cooperation within the cluster or the cluster management. The kind of the evaluation could be with the help of accelerating the information flow and the ex-post, ex-ante, formative, impact evaluation or benchmark- project generation and providing the necessary competences. ing or quality labelling. (Meier zu Köcker & Kind, 2012). More Of course, the right cluster manager cannot even substitute analyses were born even in the last few months (e. g. Joenneum the cooperation between the cluster actors and cannot replace Research – Policies Graz or The SLIM Project in Sweden). It can the essential motives of the cluster's operation but it can really be seen that Europe and the member states are different and catalyze the cluster development not only with the realization not unified. Taking the national characteristics, the ways and of the above mentioned task but with right position of the mar- the methods of the national developments into consideration, keting & branding and internationalization strategy and with companies with different conditions and structures, and then solving the problems, debates, etc. The services offered by the cooperative and competitive economics have developed cluster manager shall be colourful based on the demand and there are regions where it is worth to strengthen the ideas of habit of the cluster actors and on the activity of the cluster. The cluster initiatives with any kind of support and thereby stimulat- most important thing is that the cluster manager shall not want ing the development of the cooperation's culture and speeding to get the upper hand over the cluster. Moreover the cluster up the infrastructure development of cluster organisations and manager cannot lose sight of the fact that the cluster's success generating the joint investment projects of the cluster actors. always depends on the actors and on their original aim – to Parallel to it we have to say that there are regions where the achieve the maximum profit via cooperation.
direct subsidies for the cluster organisations are not necessary at all because the main aim and motivation of the cluster actors are the realizable certain and high profit through their coopera- Key elements – Trust and social
As it was written in the Vienna Cluster Manifesto as well ‘The It must be mentioned that a 'program' cannot be successful Commission shall further support the statistical analyses of if the interested parties do not trust each other, they do not clusters as provided in the framework of the European Clus- co-operate or they are not committed to a long term, consist- ter Observatory. … Member states and regions should, with ent strategy. ‘The ability of people to work together for com- support from the Commission, continue their policy dialogue mon purposes in groups and organizations is the social capital on cluster policy matters to further develop and adapt cluster which is a capability that arises from the prevalence of trust in a Clusters and game theory society or in certain parts of it' (Fukuyama, 1995). ‘Further 1/ building up a cartel
developed the social capital is the existence of a certain set of informal values or norms shared among members of a group There are forms of the cooperation which are successful for the that permit cooperation among them' (Fukuyama, 1999). It actors but at the same time damaging for the economy (e. g. ‘refers to the collective value of all social networks and the reducing the competition, agreement to the fix prices, market- inclinations that arise from these networks to do things for ing or production etc.). Cartels are illegal, but even so from each other' (Putnam, 2000) ‘The literature has discussed time to time the companies try to enter into such agreements. social capital as a resource at the individual, organization, and Cooperation and competition are characteristic for the relations community level' (Strauss, 2010). ‘Social capital appears to be of the cluster actors, too, but a successful cluster is not about positively related to organizational effectiveness and to play a the restriction of competition. We cannot, of course completely central role in reducing organizational transaction costs' (Fuku- exclude the possibility of parasites, undesirable groups of com- yama, 1995). ‘It also facilitates coordinated action to achieve panies that abuse cooperation and especially the support for desired goals (Leana & Buren, 1999) justifies organizational forming cooperation to reach their sinister goals. commitment (Watson & Papamarcos, 2002), and results in a significant positive impact on product innovation' (Nahapiet & 2/ no panacea
Ghoshal, 1998). But there are differences between the level of the trust and the social capital of the countries, and these dif- The well documented success-stories about the profitable and ferences could appear among the regions of a country as well.
favourable effects of the cooperation in the frames of a cluster might give the impression that joining a cluster will solve all From the point of view of this concept paper the trust
business problems. Participation in a cluster might be a more and the social capital is significant with a view to the
effective way to reach one's goals, but it should not be the goal future profit of the trust and social capital. The return
itself. Managers, who wait for such a miracle, completely miss in the cooperation invested resources is always awaited
the point and will fail miserably. Companies focussing on par- just in the future.
ticipation only will not be able to benefit beyond the obtained The present value of the awaited profit is being
decreased not only by the time-factors but by the risk
3/ herd attitude
of the distrust (e. g. changing of the economic regula-
tion, deficiency of the cooperation-rules, the problems
To found a cluster – it is trendy nowadays. Business actors often of exercising a right). The more risk is recognised by the
feel that it is more profitable to join a cluster than to let the cooperating partners the less but immediately provided
opportunity slip away. They do not really think of what this advantage (profit) make them give up the cooperation.
seriously means in practice, they are just toying with the vision of the word ‘cluster'. The idea of cluster is slowly becoming a I.7 "Cluster
illnesses"
4/ lack of business and ambitions of the
In the last decades extensive studies have been conducted to investigate and determine success-factors in clusters. During the examinations the characteristics of the clusters have been The cluster itself is an answer for the challenges of the eco- analyzed from a number of points of view. On the basis of nomic competition. Increasing the competitiveness of the com- these examinations we can theoretically and statistically specify panies the cluster gives them confidence that they will have the kinds of clusters to be funded. Such conditions can specify success in the fields of market struggle. The cluster is not a the optimal number of cluster actors or the ideal competences charity organisation, this is actually a secondary result of the of the cluster managers . Theoretically it is also possible for companies' activity. Misjudging where the cluster can help its each of us to found and build a successful operating cluster or actors can lead to bad experiences with any cooperation. catalyze the process. 5/ isolation effect
Although the theoretical models have been proved in
the practical life many times, the practical experience is
If the cluster actors do not have enough information to make not unanimous. What are the problems noticed during
the right decision on their own market position or market the last years and the policy makers are willing to hush
share, then their cooperation is suffering from an isolation effect and their results must be non-competitive in the global market. It means if there is a product in the global market, In the cases the cooperation between companies is
which is more easily and more cheaply available and moreover not the result of an organic development. In a market
it has a better quality than the product of the cooperation, then economy a company and its partners naturally have eco-
the cooperation itself is not successful. Why? Because with nomic cooperation and if these relationships become
right assessment of the economic situation and also with hav- serious and intensive then, the partners are ready to
ing marketable information and even with involving outsiders pave the way for a cluster initiative. But … the natural
in the business, successful economic cooperation – including relationships and cooperation between the companies,
the competitive products – would be easily guaranteed. the industrial condensation points which helps the deve-
lopment of clusters and the favourable business environ-
6/ growing apace with the subsidies and
ment could not guarantee the development of a success-
grant dependency/rent seeking
ful and a self-supporting working cluster in an examined
area. On the one hand there are clusters recognised,
Getting subsidies for cluster development – this is the main which operate at industry concentration points, have
business of the cluster, therefore the profit increase comes only a suitable company size, supporting environment, a
from the subsidies. successful cluster manager etc. and are not successful
despite these facts. On the other hand other clusters which
do not operate under above mentioned circumstances
and thus should in theory die, in practice flourish. These
The spread of this behaviour, getting the benefits of the opera- facts suggest us to look deeper into the incentives in the
tion of a cluster without any willingness for real cooperation operation of a cluster. After all, what drives the cluster
could jeopardize the success.
and its actors?
8/ extremes
The overconditioning and overregulation of the cluster's opera- tion, the elaboration of complicated rules of procedure, the forced and unnatural increase of the cluster actors' number put high risk even on the operation of a successful cluster. Game theory studies strategic conflict situations. What are the crab sandwich they realise that they have some common inter- characteristics of these situations? Firstly, the parties are selfish: ests: B could help company A to materialise this brilliant idea. for a conflict of companies this simply means that they want For reasons that we do not need to go into here B's help is to maximise profits although in general the utility of the con- not enough, at least two companies of this type are needed. flict's outcome can manifest in various non-monetary forms, Fortunately B has contacts with C and D, either of which can too. Secondly, the conflict's outcome depends on the parties' serve as a second company, in fact A, C and D could also realise actions. We call the conflict situation a game and the involved the project. The CEO of A finds the plan good and suggests parties the players. The name probably comes from the fact to share the expected extra profit of 12 million to be shared that the father of game theory, the Hungarian genius John von equally among the four actors of this cluster. Will this work? Neumann was originally interested in developing a mathemati- cal theory of bluffing in poker and his mathematical results The shortest answer is: No. If the companies A, B and C can found applications in economics and beyond only years, dec- also do the project and obtain the same profit it would be fool- ades later (von Neumann & Morgenstern, 1944).
ish to include D in the project and pay it 3 million, wouldn't it? OK, D can stay on board, but with a much more modest The strategy of a player determines his actions for every possi- share of the proceeds. Oh, but the same argument applies to ble game scenario. As a result, given the strategies of the play- B, or C that are of the same "type" of company as D. So, as a ers, a game can be played and the outcome can be determined matter of fact A takes all and the substitutable members of by a mediator or a computer. Therefore the payoffs, such as the group get almost nothing. Moreover, even over the little profits of the players can also be determined once the strate- payment they would get, the would start an eternal battle any two of these trying to skim the third company by kicking it out if the business. We can describe a game in various forms, but there is one dif- ference that divides games into two groups: cooperative and We have only leaped over a tiny detail. A has no contact with non-cooperative games. The difference is in the legal environ- C or D. A can only cooperate with these companies if B helps ment: noncooperative games are played in anarchy, in an en- it, if B is on board, if you like: with B's permission. While com- vironment where agreements are only kept if the parties are panies A, C and D could realise the project, such a cooperation interested in keeping them. In cooperative games, on the other is simply not possible. But then B has a new, special role: B can hand we assume that it is possible to make binding agree- connect A with the right people. If we look at it again, there ments. This distinction is largely due to Nash, who made key are only two ways the project could be realised: A, B and C or contributions to both types of games (Nash, 1950, 1953). While A, B and D. As C and D can substitute each other, they will not the language of the two types of games is remarkably differ- get much of the (extra) profit, the profit is shared between A ent researchers have shown that the conclusions drawn from and B. They can share the profit equally as 6–6 millions, but if the two types of models are essentially the same. The different any other distribution emerges neither of them will have the formulation, however means that the two types of games are possibility to increase its share. After the offer of company A, B used for different situations: noncooperative games are best getting 9 millions is a likely outcome, for instance. suited to study the detailed interaction of a few players, while cooperative game theory can handle the interaction of large We have noted that C and D are perfect substitutes, in other groups of players. Since a cluster is a selfish cooperation of words one of them is superfluous. So why did B suggest two economic agents, cooperative game theory is the better suited partners at the first place? Consider the same setting when D of the two to study the interaction. Nevertheless we start with is not there: Then only full cooperation of all the parties can a few simple concepts from noncooperative game theory that, realise the project. In such a setting B's role as intermediary is on the one hand illustrate the modelling power of game theory secondary, company C can rightly demand a share of the profit better, and motivate our use of cooperative game theory later. and this share is a loss to A and B. In other words A and B profit But before we move on to the theory let us consider a simple from having both C and D in the cluster. Finally note that the assumption that a company will cooperate Company A has a brilliant idea that could be developed into a for zero profit might sound unrealistic. Of course this is zero very successful and profitable idea – with the right partners. economic, rather than accounting profit where the company The CEO of A meets the CEO of B at a reception and over a has been compensated for all production costs as well as its opportunity cost (the cost of doing this project rather than in- Suspect 1 Suspect 2
vesting its resources elsewhere) and a compensation for risk. Getting a zero profit is therefore not the same as not getting paid, but a higher profit is naturally preferred. In practice a zero 1 Prisoners' dilemma profit case will not arise due to imperfect substitutes, capacity constraints or switching costs, but these only mildly affect our By the solution of such a game we mean finding the strategies the suspects (or players, in general) will choose. The difficulty in finding the solution lies in the fact that the outcome and the As we have said this story is simple, but real clusters have simi- payoffs depend on the strategy of both players. In other words lar, though naturally more complex interactions, where the a player must choose his strategy making some assumption same arguments could be used. In the more complex cases, about the other player. however the calculations may be a little more involved requir- ing a more general and more formal treatment.
The inspection of the game in Table 1. suggests that the players should choose (Deny, Deny) to get the highest utility. Unfor- tunately these are criminals, so they might ignore a possible II.1 Non-cooperative
agreement before the questioning they might act differently. Indeed, if any of the suspects chooses the strategy Deny, the A non-cooperative game consists of three elements. Firstly, N other profits from Cooperate. Since the argument applies to is the set of players {1,…,n}, with a generic element denoted by both criminals, it is not very realistic to assume that any of them i.The set of strategies available to player I is denoted by ∑. and will think (Deny, Deny) is realistic. If one criminal chooses Co- we denote a particular strategy by σ .1 A strategy profile σ is the operate, the other's best response is Cooperate, too. This also collection of all the individual strategies. ∑ collects all possible means that if they agreed to (Cooperate, Cooperate) neither of strategy profiles. The utility of a player determines the payoff them would have a reason to act differently. This is precisely of the player given the entire strategy profile. So, for instance, the equilibrium we are looking for. if the players have chosen the strategies σ, the payoff of player i is given as u (σ).
We call a strategy profile σ* a Nash-equilibrium of a game, if the strategy chosen by any of the players is a best response to First we explain the so-called Prisoners' dilemma. The story the strategy of the others. Mathematically: goes as follows: after a bank robbery two suspicious persons are captured with illegal weapons. The police has no evidence ui(σ*)≥ui(σi,σi*) for all σi.
that they committed the crime, so the two suspects are inter- rogated at the same time in separate rooms. Four scenarios Situations involving public goods often resemble the prisoners' are possible depending on whether the suspects cooperate dilemma. In a cluster the public good is a joint project, where with the police or deny the crime. If they both deny, the police the actors of the cluster can choose an effort level to contrib- does not have evidence, so they must be released with minimal ute to this project. While choosing a high effort would be bet- charges for the illegal weapons. If they both cooperate, they ter overall, the individual actors prefer to free-ride on others' can be charged with the robbery, but get some reduction of efforts and spend own resources on own projects ultimately the prison sentence for their cooperation. If on the other hand leading to the breakdown of the project and a dysfunctional one of them cooperates and the other denies, the first is set free for the cooperation while the other is put to jail for a long sentence that is made even longer by the refusal to cooperate In real life we do see public goods realised, and cooperation is with the police. In the following table we present the game often possible in similar prisoners' dilemmas. How can be res- in normal form, in each case the first value is the utility of the cue cooperation? A suitable legal framework using hefty fines first suspect, the second is that of the second suspect in this can change the payoffs so that shirking is not a best response. outcome. A longer prison sentence is represented by a smaller We return to this topic in the following section. As the legal utility (a negative number with a larger absolute value).
framework is never perfect, the enforcement may come too late, we may wish to look for self-enforcing mechanisms to maintain cooperation. 1 To be precise these are the mixed strategies that include a randomisation over the so-called pure strategies S. If the interaction lasts for more the one encounter the utility rather than the means to achieve these. At the same time the from a decision must also include the utility from future so-called Nash program works on showing that the very same encounters. Mutual trust and mutual cooperation can be results could be obtained as equilibria of non-cooperative rewarded by future trust and cooperation. If the probability of games. Put it simply: we can say that cooperative games are future encounters is high and value of future money is high result, non-cooperative games are method oriented. (the inflation is not too high), it is less likely that a one-time defection and the corresponding high payoff is greater than In the following we introduce the basic ideas and terminology the value of future cooperation. of cooperative games.
Note that this value of future cooperation is only there if the We still have a set of players and this set is denoted by N. Sub- game is played repeatedly forever or at least is repeated with sets of this set, that is, groups of players are the coalitions. high probability. A cooperation with a definite or likely end Actions, strategies are implicit and are limited to choosing play- does not help: in the last period the cooperation breaks down ers for cooperation. Instead of a utility function for individual removing the incentives in the previous period to cooperate, players, we have a value V for each coalition (Figure 3). The idea of this value function originates from von Neumann & Morgenstern (1944) who determined this value assuming that II.2 Cooperative
if a coalition C forms the remaining players play against this coalition. Whatever C is guaranteed to make from this situation The main difference between cooperative and non-cooperative is its value. Now we simply give the value of each coalition. games is that in cooperative games players can make bind- If we also make the assumption that members of a coalition ing agreements, i.e. agreements they must keep. In coopera- can arbitrarily share this coalitional value then we talk about a tive games the interest is on the formation of coalitions (see game given in characteristic function form or simply a transfer- Figure  2) and on the sharing of the benefits of cooperation able utility (TU)-game.
2 In cooperative games strategies are limited to the choice of cooperation. In this example the player makes a choice between the "red" and the "green" coalitions – or staying with the ("blue") grand coalition.
3 The characteristic value of the "red" coalition is classically defined as the minimal value obtained when playing against the complementer coalition, that is, the coalition of the remaining players What is the solution of such a cooperative game? In purely For the sake of this example consider a cluster producing cooperative games we assume that the grand coalition forms and selling furniture. Some of the actors specialise in office, where all players cooperate and the solution only specifies how kitchen or children's furniture, others in marketing, logistics or the players will distribute the value of the grand coalition. In producing brass parts. It is natural to assume that the brass some situations this assumption may be too restrictive. If, for part manufacturers could form a (smaller) cluster themselves instance we want to know if a group of regional companies and share technology, buy and sell in large quantities etc. etc. should form a cluster, we may also want to know if all these such a cluster clearly has some potential benefits. Now suppose companies have incentives to belong to the cluster. In such a that the furniture cluster generates some extra profit thanks case the problem is two-fold: which coalitions form, and how to costs savings and extra trade generated. How to share this do these coalitions share their values among their members. extra profit? For the moment we will focus on games of pure cooperation. An imputation is a distribution of the payoff of the grand coali- Of course one should not imagine a pile of banknotes or a sum tion among its members, such that each player gets at least sitting on a bank account: the money is often of the forms as much as it can get without cooperation, that is, as a single- of cost savings that may be realised unevenly. If therefore the player coalition.
brass manufacturers feel that they get less than what they could make with the same facilities outside the present cluster, As there are no strategies in these games, the equilibria defined they might demand a higher share or threaten to leave the clus- for non-cooperative games are of no use. There are at least ter. The higher share of the extra profit is probably in the form two types of solutions and two very popular solutions: the core of higher prices in the contract for brass parts. Is this attractive and the Shapley-value. Before we move on to a more formal for the rest of the cluster? Well, the rest of the companies could definition we provide the intuition of these concepts by means also buy the parts from other sources. If the cluster is worth of two simple stories. more than its parts – it is superadditive – then an agreement is always possible. Quite similarly, each group of actors: mer- chants, kitchen makers, small companies, large companies, etc. could – and should – consider its outside options. We say that the allocation of the extra profits is in the core if all these com- is not very favourable for A1: it practically must build the whole panies find the allocation reasonable and they cannot – justifi- mall with high costs, while A89 may incur no extra costs at all ably demand an increase of its actors collective share. despite a long list of special requirements – already satisfied thanks to actors coming earlier. To make this fair we consider For the second example consider a cluster of companies build- all possible numbering of companies – there may be very many ing and using a shopping mall. Different shops or groups of such numberings – and take the average contribution. shops might have different preferences. The luxury shops insist on the marble pavement, the banks want to have high security Academics widely consider these methods as acceptable ways measures, the hypermarket an easily accessible shopping mall, to share the profits and in fact such metods have been used the cinema the late opening hours. Each of these demands in- for building airport runways (sharing the costs among land- crease the total cost of the project. The question is: how to ing aircraft, (Littlechild & Thompson, 1977)) or managing the share the profits when we know that the costs depend on the Tennessee river (sharing the costs among nearby farms, ship- actors' wishes. One possible method is to use the core again, ping companies, and cities in the Tennessee Valley (Straffin & but in this setting the Shapley value is more natural. For this Heaney, 1981)) among others. In the rest of the section we number the actors as A1, A2, etc. First assume that only A1 present a short technical summary of these two concepts. This builds and operates the mall. The costs will obviously be lower, section may safely be skipped, this will not hamper the under- but so will be the profits. The difference (possibly negative: a standing of our paper.
loss) is what A1 could obtain on its own Now take A2 and see what does it add. The two companies need a somewhat bigger The core (Gillies, 1959) is the cooperative equivalent of the mall, may attract more customers, so we can again calculate Nash equilibrium, but it allows also for coalitional deviations the value for the two-company mall. The contribution of A2 is (Figure 4). The core collects imputations such that for all coa- the increase of the profit with respect to the single-company litions it holds that the total payoff paid to members of this mall. Note this amount next to A2's name. And so on for A3, coalition are equal to or higher than the value of the coalition. A4, etc. This row of numbers tells us how much each of these Were this not true, the coalition would not sign the agreement, companies added to the value of the project. Clearly, this order but rather operate on its own. While it may seem rather dif- 4 In the core no coalition of players benefits from forming and leaving the cooperation.
5 The Shapley-value takes the average marginal contribution of a player. For this all possible orders in which a coalition may have grown are considered.
6 A coalition has no structure 7 There may be many different network structures supporting the same coalition. Networks a), b) and c) all support the coalition in Figure 1, while network d) is disconnected and therefore cannot support the same coalition.
ficult to satisfy the demands of all coalitions most games have A whole stream of literature has been motivated by the poten- many imputations that satisfy them. Unfortunately there are tial emptiness of the core either to see what happens in the also many that do not have any. We say that the core of such game if the core is empty or to somehow save cooperation. For games is empty. So-called balanced games have non-empty instance the minimal dominant set (Kóczy & Lauwers, 2007) cores (Bondareva, 1963; Shapley, 1967). To have an empty core contains imputations that emerge dynamically after playing the means that the total resources available to the grand coalition game for long. Approximate cores (Shubik & Wooders, 1983) are not sufficient to simultaneously satisfy the coalitional de- take the costs of forming/breaking agreements into account: when these costs are high, higher than the gains from leaving the grand coalition, cooperation survives.
The sharing aspect of imputations is better expressed by the Shapley-value (Shapley, 1953), that pays the marginal contribu- tion to each player. It can be best understood by a story: Initially Coalitions are a greately simplified version of reality as they lack the first player has its own value as a single player coalition internal structure (Figure  6). In some situations the structure .The the second player arrives and it contributes the difference of cooperation has a role, too. Where personal connections between the value of this duo and the first player's single player or trust play a role only cooperation between parties that are coalition, and so on (Figure 5). We then take all the n! possible connected to each other personally or who trust each other are orderings of the players and take the average of a player's mar- possible. In such situations a player can have a high value simply ginal contributions. for connecting other, productive players (Borm, Owen, & Tijs, 1992; Herings, van der Laan, & Talman, 2005). The core can The Shapley value is never empty, it is always defined. (Dubey, also be generalised to games where the connections among 1975; Neyman, 1989; Shapley, 1953) and others have shown the players are important. For such TU games over a network that the Shapley value determines the only way to divide the we must have a value function and know the underlying net- total coalitional value if we require some simple, often elemen- work of players.
tary properties, such as symmetry, to hold. The Shapley value gives a fair way to share the coalitional payoff, but it is not In network games only coalitions that are connected make sense always a stable way. The Shapley-value belongs to the core in (Figures 7a-c and 8a). A disconnected coalition (Figures 7d and so-called convex games (Shapley, 1971), but it may well be that 8b) means that some of its members cannot communicate and the core is not empty, but the Shapley value is outside the core. therefore coordinate. Such a coalition then clearly cannot form. In such games the allocation that is considered fair is simply not accepted by all coalitions.
a) Feasible coalition b) Infeasible coalition 8 Coalitions under network 2a. The coalition in Figure 3a is connected, while Figure 3b is not. Members of the coalition on 3b cannot communicate and are therefore not a threat. III Cluster
By now it may be clear that game theory, especially cooperative ural choice. Since the participating companies and institutions game theory, models conflict situations very similar to those are naturally interpreted as players the question that remains that can arise in a cluster. Over the decades researchers have is how to find the coalitional values, that is, the characteristic written hundreds, possibly thousands of papers researching function. In other words: what is the value of a coalition? these games, providing ways to "solve" these games, that is, acceptable ways to solve the conflict among the players as well We see two possible interpretations: (1) Projects as coalitions as describing properties of these games that guarantee, for (Figure 9) or (2) Clusters as coalitions (Figure 11). instance, that a conflict can be a win-win situation. In the following we formalise the connection between coop- III.1 Where are the coalitions in
erative, so-called TU games and clusters making it possible to use the enormous literature written for games to be used in the study of clusters. The ultimate purpose of this exercise is Projects as coalitions/coalitions as projects
to translate the game theoretic properties into golden rules for cluster evaluation.
A project is a form of cooperation among actors of a cluster that has a clear project plan, project objectives and an estimat- Our aim is to evaluate clusters by game theoretic means. This ed project profit. This project profit is the value of the coalition. requires first the translation of the problem into a mathematical What are the advantages or disadvantages of this approach? format, solve the problem using game theoretic methods and translate back the results into practical recommendations. The single most important aspect of a project is that it is something specific, material and therefore the profitability of We are interested in the possibility and nature of cooperation in a project is a natural question, something that is also raised clusters, so modelling clusters by cooperative games is the nat- by the participants already before joining the project. On the Projects as coalition
9 Projects as coalitions 10 Balanced collection: The members of the blue coalition are committed to it, while the members of the purple coalitions share their time between two such coalitions each. other hand we do not only look at the behaviour of a cluster in Clusters as coalitions/coalitions as clusters
the present, but would also like to understand future contin- gencies. For that we would need information about future or In general a cluster is not created for a single project nor for a even potential projects. For such projects the same information small set of projects but rather to be an incubator for new ideas is not available or is not accurate. In a cluster it is perfectly natu- ral that a cluster actor will participate in multiple projects and share its time among these activities. This behaviour is not nat- Basing our calculations on current projects only can be very lim- ural in cooperative games, coalitions do not generally overlap. ited and may only be indicative of the minimal potential of the cluster. So instead, we see a coalition as a cluster, possibly with Overlapping projects can be modelled by so-called (balanced) some ongoing projects, but also with the potential for new collections (Figure  10). In a balanced collection each player projects. The value of a coalition is then the present value of all spends the same amount of time on the projects including pos- future profits coming from the projects from within the group. sibly a project that does not involve other players. The limita- This value is comparable to the value of a stock that is also seen tion of this setting is in the assumption that a project requires as the present value of the future stream of dividends. the simultaneous cooperation of the players, in other words, actors of a particular project/coalition must spend the same This second concept is much more general. While it clearly amount of time on that project/in that coalition. This is clearly includes the value of a project if the set of participants coin- a restrictive assumption that will not typically hold in a natural cides with the coalition, it also allows for other projects by sub- sets of the coalition members. As a special case it includes the profit from singleton projects, that is, from projects that do not need cooperation with other players. On the other hand it does not include the profit of projects that require cooperation with outsiders. The complexity of this approach is also its disadvan- Clusters as coalitions
11 Clusters as coalitions tage. Just as there may be disagreements about the value of whether the fundamental assumptions of game theory also a stock, the value of such a cluster-coalition is also difficult to hold in the setting of industrial clusters.
determine. Especially that the definition of the game requires an exponential number of such valuations. In the following we outline a set of questions and hypotheses corresponding to these basic assumptions. If these hypotheses are tested to be valid, a rather standard game theoretic approach III.2 About translating clusters into
can be used. If some are found false we may still use the model, but with certain modifications. If many of these assumptions are false, new richer models need to be developed. We must Game theory is a branch of mathematics with widespread note that this is a very unlikely case and once again point at the applications in business and economics as well as many other numerous applications where the game theoretic approach has disciplines from biology to politics. Being a theoretical science already proved itself useful. its models live not even in sterile laboratories, but in the ide- alised realm of sets and factorials and Greek letters. Real Life In the first group of hypotheses we focus on the fundamentals. must surely be more complicated! Has such a model anything to do with reality? As a first prerequisite we would like to understand what drives clusters, what drives the formation of clusters. We depart We believe, it does. In fact, it is not only us, but the ocean of from the usual principal-agent approach where the conflict is working applications prove that on the one hand people, but between the owners and the managers of a company as clus- especially companies can very well be modelled by the homo ter actors are often too small, owners are often the managers oeconomicus, the selfish man and on the other, that game the- as well. We expect the dichotomy to lie between the profit ory is flexible enough to accommodate small deviations from or value maximising totally rational faceless investor and the the standard setups. Is this also the case for clusters? While we entrepreneur who is driven by creativity, by the joy of creating are quite optimistic, one has to carefully check and investigate something new and the joy of collaborating with others. We do not say that the two aspects cannot live along each other, and organisations. Several companies and research groups are but before going any further we must understand if the cluster in the race to come up with the first working model. While is a means to reach a higher profit level, to collect previously there is a lot of uncertainty in the patent race, three things are unrealised profit or it is perhaps the goal itself.
clear: the company that can file the patents first takes most of the market, the rest may have spent large amounts of money The motivation for this question is clear. While some clusters on the research, but most of this has just been wasted, and kick off with intense co operation, with very clear goals and money can accelerate the research process. So if you put in objectives, there are clusters founded by friends and schoolmates more money, you are more likely to win, but if you lose never- with the aim of co-operation with old acquaintances hoping theless, you lose more. that something useful comes out of it – and in the meantime the collaboration is fun, all will enjoy business lunches. This is a lot like the dollar-auction, where a 100-dollar bill is auctioned away, but with the catch that all bids, including los- The formation of clusters is supported by national and EU insti- ing bids, must be paid. Here the prize is the profit made with tutions. In extreme cases obtaining this support can be the goal the product, while the bids are the research costs. Once one itself. Naturally all clusters must have a project, such clusters enters the dollar auction, it is difficult to stop. The difference have such projects, too, but the realisation would be possible between a winning and a losing bid is just a few dollars so if without the formation of the cluster. Such a cluster is clearly we compare this with the prize, it is surely worth putting it in. If about money, so it clearly belongs to the first group, where the all actors think this way, however, the bids can go way beyond aim is maximising profits, and the national or EU support is just the 100 dollar figure – we may see this in the research game, one way to realise this. too: Once in the patent race companies try to avoid being a close second either by quitting the game early or by outbidding A company is approached by another company to do a joint the others. project. The offer covers all project-related costs (including standard profit rates to satisfy investors) plus 1% of the remain- Our interest in these issues is twofold. On the one hand – relat- ing profit. Rationally the company should accept the offer since ed to hypothesis 1 – we would like to understand what drives every bit of extra profit is great. In practice, however, the com- cluster actors, what are their objectives. On the other hand, in pany may be offended by the small share and ask for more or order to use mainstream economic and game theoretic models reject it. This example of an ultimatum game illustrates that we must have companies that are rational (in an economic, that economic rationality cannot be taken for granted. is: homo oeconomicus sense), companies that work on maxi- mising their profits and make well-informed decisions with this Hypothesis 1. Companies join clusters as a homo oeco-
nomicus, with the intention to harvest profits that
could not be harvested otherwise. Other factors, such
If our hypothesis is false, not all is lost, but a formal analysis of as the joy of creativity and collaboration facilitates this
strategic decision making would require more complex math- co-operation but only play an auxiliary role and can be
ematical apparatus.
expressed in financial terms.
Hypothesis 2. Companies take conscious decisions when
joining clusters and this decision is just as formal as the
III.3 The bases of decision making:
decisions when joining any other co-operation.
Do actors like profi t?
So what are the pros and cons of joining a cluster. On the one Irrespective of the answer to the first hypothesis we would hand actors of a cluster expect profits from projects that would like to understand the mechanisms that result in a company or not realise otherwise or from economies of scale or scope real- other legal entity joining a cluster. We would like to know to ised through the cluster. What are the costs on the other hand? what extent can these mechanisms be considered as formal. The costs of running a cluster initiative or cluster organisation Do companies use formal protocols before such a decision is are not substantial when compared to the possible benefits. Even if all these costs are for nothing, the losses are not severe so however small the probability of realising the foreseeable The next generation solar panel will be a massive hit: govern- profits is the benefits outweigh the direct costs. There are how- ments provide better and better incentives to reduce energy ever other costs, too. A cluster can only become an incubator usage, and on the other hand their high efficiency might mean for new projects if the actors share confidential business infor- that installing them will be a profitable decision for many homes mation. The cost here is sharing this information.
One thing that is not clear is how deep the economic analysis of As a technical detail we would like to understand how compa- these companies is. Consider a company making funny T-shirts. nies handle future profit streams. Two aspects are considered. Creativity is costless so the price of such a T-shirt is really just First: the possible sources of income. Clusters are there not the cost of the T-shirt (for simplicity we say this is 0) plus an only to create a formal environment for current projects and arbitrary markup for the creative design. Suppose this markup co-operations, but as an incubator for future ideas, for future is somewhere in the range 1 … 00. The company knows that projects. In fact, clusters are not needed to complete ongoing there are many similar shirt-makers around, and they will lose projects. Do companies understand this difference and include customers unless they sell significantly below the average price, future projects in their cost-benefit analysis? but make as much money as possible. Say, around half of the average price of similar funny T-shirts. How much should it Hypothesis 4. Cluster actors attach value to projects in
value its creativity? What should we say? the cluster that are not yet realised.
This is a well-known game that has been asked at various audi- How is this value estimated? On the one hand companies have ences, but the patterns are always the same. There are some difficulties even to estimate the value of current projects, how fifties, twenty-fives, … ones. What is the good answer? Let us could they have estimates the value of projects they do not say right now that the correct answer is very difficult, as we even know who are they with or what will the contents be. will see it from the following argument. The naive company Such detailed information is difficult to obtain and are super- will just say: we have no info about other prices yet, so we ficial. We would, on the other hand understand the long-term might as well choose any number. This is the level-0 argument. expectations of cluster actors: do they expect similar profits The level-1 argument is a little more sophisticated: Since no from their cluster participation even after the current projects T-shirt can be more expensive than $100, if we want to be have expired or beyond the current projects? Do they expect among the cheaper half, we should never say more than fifty. less or more? How much less or more? It is important to stress Those saying fifty probably think level-1. The level-2 argument that we do not need to check the validity of these estimates, goes further. Since nobody will sell for more than $50, we can we only need to understand the information that the compa- only be much cheaper than the average if we do not sell for nies base their cost-benefit analysis on.
more than $25. But then the argument can be repeated and the level 3–4–5– … arguments claim that one should never sell The profit from (present or) future projects does not come at for more than (rounding the numbers) 13, 7, 4, 2, … 1. If all the time of the investment. How is this profit stream aggre- the companies are fully rational one can only remain competi- gated so that it becomes comparable to the costs that occur tive if the price is 1. Is this the best way to make profit? Is this at the time of the decision? (We realise the future projects will how the company makes the most profit? Most likely not. The require project-specific investments that are subtracted from company choosing this price is clever enough to make such a the incomes realised at the same time; the profit is the differ- high-level argument, but fails to realise that not all companies ence of the two that can at times be negative.).
are equally sophisticated. A sophisticated company will realise not only that the argument does not stop at 50, but also that We consider two possible scenarios. Companies base their some other companies do not go further. For an accurate an- decisions on predictions for a finite horizon, such as for the swer we must think how sophisticated our competitors may be. coming 3–5 years. For this limited horizon it is still possible to This depends on the composition of the decision makers, but make relatively accurate predictions based on data and models for a general crowd 12 may approximately be a good answer used for "standard" business plans. Longer estimations require (so long as not too many people read this text). additional data and perhaps more refined models, the cost of which outweighs the increased accuracy of predictions.
This example illustrates the importance of understanding how sophisticated the actors are. While such a detailed analysis is Ideally, however, and this is the second option, the present not necessary a number of simple hypotheses clarify the basic value of an infinite income stream should be considered with appropriate discounting. This approach is not only useful math- ematically, but is –theoretically- the common practice to cal- Hypothesis 3. Companies do a cost-benefit analysis com-
culate the value of a company with publicly held shares or of paring the cost of sharing confidential information with
a real estate. The difficulty lies not only in the estimation of other cluster actors and the foreseeable benefits from
future profits, but also in determining the discount factors. The discount factor can incorporate, besides the devaluation of cur- rency also the decreasing probability that the cluster will exist or that the company is still part of the cluster.
In practice we expect a compromise between the two The first thing we note is that such a code is essentially about approaches limiting a horizon, but discounting future profits. the distribution of the profits of the cluster. While the code can How do companies treat future profit streams? specify property rights or hierarchies these all have monetary values and can be expressed as payoffs. This is especially true Hypothesis 5. The value of a cluster for a particular com-
for the allocation of such rights or duties when applied to pany is discounted money-stream within a given time
future contingencies. horizon with a discounting reflecting the depreciation
of the currency as well as the probability that the project
In our first hypotheses in this section we look at the nature of or stream of projects will be discontinued.
cluster codes. We believe that a project does not start until pay- offs are specified for all contingencies. This really means two Given our hypotheses about the way companies make deci- things: firstly, that companies, when starting a project, realise sions about clusters we can move on to the decisions about the possible alternative project outcomes. Put it simply: they forming a cluster. Some of our hypotheses will likely be false: realise that the project can be failure producing a loss, a success this will influence our models to some extent, but, as we producing a profit, it can be a huge success producing a profit have indicated earlier already, this does not normally turn our beyond expectations and at last it may create a benefit even approach invalid. success, but different from the expectations. Does the code specifiy contingencies for all possible outcomes? III.4 Cluster code – structure:
Hypothesis 6. The cluster code addresses alternative out-
Do actors think about present
and future alternatives?
Note that the alternative outcomes may be due to external, but also internal circumstances or events.
In the following we state a number of hypotheses about the cluster code. Some clusters do not have a formal contract, but It is also important that the code does not only recognise the operate more on a club-like basis. In such a case by contract alternative outcomes, but that it provides rules for allocating we mean a collection of formal and informal agreements that profits (or losses) for all possible states of the world (up to rel- are nevertheless commonly known to the actors of the cluster. evance to the cluster). Do actors consider "unlikely" events In the code we also include the general framework support- when making decisions? ing the writing of contracts for projects that do not include all actors of the cluster. Such a framework does not only pro- Hypothesis 7. The cluster code specifies contingencies
vide a possible legal aid, but outlines the general principles of for off-equilibrium or non-ideal outcomes too.
the cluster. These principles determine not only the current contracts related to current projects, but form the basis for Let us stress the importance of Hypothesis 7: If this Hypothesis future contracts related to future projects. In sum, by cluster is not true profit-seeking companies might join a seemingly – code we do not necessarily mean a written, legal code, but the for them – disadvantageous cluster expecting a different out- de facto standards of behaviour regarding present and future come that, on the other hand, is favourable to them. Instead, agreements. We must underline the crucial role of the cluster companies must see clusters as a full package, making a deci- manager in creating and – in the absence of a legal document sion that is rational regarding the entirety of the code. addressing all issues below – maintaining and enforcing this Setting the golden rules IV Setting the golden rules
Having clarified the basic framework for decision making and Hypothesis 8. A company only joins a cluster if this brings
having thereby made the connection to game theory we can now move on to discuss the cooperation-related decisions a cluster actor company must make. Understanding the incen- While some of the well-known clusters overseas have emerged tives of the individual companies we can discuss properties in an organic way, in Europe it is common to expedite the pro- of the cluster they constitute. In particular we may be able to cess with a top-down approach, "creating" a cluster. While translate game theoretic concepts into golden rules of cluster we do not want to speculate on the particulars of this pro- evaluation. As an ultimate goal our model could produce quan- cess there will be a point when a company makes a decision titative predictions about a cluster's expected performance or whether to join a particular cluster and at this point the cluster is either already existing, or is already forming, but already in this latter case the scope of cooperation, the possibilities for joint projects as well as some of the cluster code is known. In IV.1 Joining a cluster: Do actors
sum, the company has some information – however vague – on the prospects with this cluster. look for profi t?
Now that the structure of the cluster code, directly or indirectly Given that joining a cluster involves some costs, too, one specifying payoffs in all world states is given we can move on should normally investigate other alternatives. For the moment to the strategic decisions of the companies. suppose that a company has the possibility of joining one of two clusters. Of course it should join the one that brings higher The first property, Hypothesis 8 is very natural. This corre- sponds to individual rationality in game theory and is a usual precondition for solution concepts. 12 Only join a coalition for extra profit 13 Choose the more profitable cluster Hypothesis 9. If a company has the possibility to join one
a more general condition regarding the choice among multiple of two clusters the company will join the one that results
in higher payoffs.
Hypothesis 10. A company should join the most profit-
Note that in general companies may join more than one cluster able of all available clusters.
and sometimes they do, but this is rare for companies with a profile corresponding to the main profile of the company.
This property is known as coalitional rationality. It has two direct implications that are corollaries of this hypothesis, but, So far our hypotheses are hardly more than concompanyations to be more explicit about these, we state them as separate of standard assumptions or perhaps some elements of a deci- sion making process formalised into a statement. Hypotheses in the following are far less obvious and while the statements Hypothesis 10a. A company should leave the cluster if a
are stated as hypotheses, we do not expect that all will be more attractive participation offer becomes available in
accepted. In any case, we must note that if some of these another cluster.
hypotheses are rejected that can, in itself, have severe conse- quences for the behaviour of the cluster. The word "leave" is to be used with care: being an actor of a cluster means that there are rights and obligations. The code In the aforementioned scenario, where clusters are created in of the cluster, by Hypothesis 7 specifies these for the event of a top-down approach companies rarely have possibility to con- departure, too. Once joined the cluster, a company must take sider joining more than one cluster. A typical company will be the possible punishments into account when contemplating on invited to some meeting with the prospect of joining a cluster the departure. The more common use of "leave" – and this is whose code is either already clear or is shaping up. Yet, a our understanding – is before joining the cluster, so it is more rational company should, before joining a cluster, do a full anal- about leaving the negotiations. Here no commitment has yet ysis of its options. By Hypothesis 8 it should only join a cluster been made, so a company will naturally be attracted by the that brings additional benefits. The following statement adds more advantageous terms. Setting the golden rules This is also true if the better offer comes from within the clus- As a minimal requirement the cluster must be more valuable ter. Indeed, most clusters have far more actors than a typical than its parts put together (superadditivity at the top level is project requires and therefore a cluster consisting of only part called cohesiveness), but, as we will see this is not sufficient, of the actors of the original cluster (for a clear distinction we call the game defined from the problem must also be balanced the smaller cluster subcluster) would typically be a profitable (Bondareva, 1963; Shapley, 1967). First we state a natural con- cluster, too. While one often thinks that the whole is more than dition that corresponds to coalitional rationality in game theory the two parts, crowding effects or the higher costs of manag- and that defines the core.
ing a larger organisation creates real life situations where the part may be more successful.2 In game theoretic terms we say Hypothesis 11. The code of a cluster ensures that the
that the game is not necessarily superadditive, that is, adding gain of any subcluster exceeds its profit as an independ-
up parts does not necessarily create additional value. ent cluster.
Hypothesis 10b. A company only joins a cluster if none of
A few notes regarding this hypothesis. Firstly, it is important the subclusters offer better prospects.
to emphasize that a subcluster does not need to secede or even organise itself to start a protest to get its share. Getting as much as it can obtain on its own is a right that must be IV.2 Cluster code: How to keep all
respected by all parties to facilitate cooperation. This is a bit like a seat on an airplane: it is very rare that someone else takes our cluster actors happy at the
seat as such an action would usually lead to a conflict where he same time?
or she must give up the seat anyway. The same holds here. No fights are required as the rights are respected. A good cluster In section IV.3 we have looked at the structure or "shape" of manager can ensure that the allocation of the profits is such the cluster code. Now that the basis on which the companies that the conflict will never arise. To do this the cluster manager joining decisions are made have been clarified we return to must be very familiar with the companies' potentials for coop- the cluster code, more precisely the distribution of the cluster Secondly this innocent condition is actually a family of a huge It is clear that there is no point in setting up a code that is number of conditions for a typical sized cluster. The number of not acceptable to the actors. If the cluster cannot provide bet- possible subclusters grows exponentially with the number of ter prospects than other clusters or its subclusters, some of its cluster actors: the addition of a single cluster actor doubles the foreseen actors will not join. number of conditions. Can so many, to a great extent conflict- ing conditions be simultaneously satisfied? Clearly, if the overall We must handle two problems (corresponding to Hypotheses gains are less than the total gains of some non-overlapping 10a and 10b) separately: External threats are somewhat more subclusters (a partition of the cluster actors) this is not possible. difficult to study as the threat is often not even on the map, Unfortunately there are cases when the gains of the cluster by but on the other hand the general industrial organisation (IO) far exceed the gains of such non-overlapping subclusters and literature already addresses the issues of competition between still the ideal, stable allocation of the cluster profit is not pos- companies. The competition for a particular cluster actor is, to sible, or in game theoretic terms: the core is empty. a great extent an issue of competition among substitutes, that is, companies that offer similar products or services. In our con- Even if the core is non-empty not all allocations are ideal. Can text the complementarity comes in the form of clusters being such a cluster be saved from falling apart? The good news is able to cooperate and produce profits with a given company. that it can be. A series of carefully orchestrated changes in the code of the cluster will always lead to a stable allocation (a so- In the following we look at the internal threats, that is, internal called imputation in the core), moreover the number of such conflicts of interests that may destabilise the cluster. Ultimately changes is only proportional with the number of cluster actors we want to understand what makes a cluster stable against and not the conditions in Hypothesis 11 (Béal, Durieu, & Solal, such destabilising forces. 2008; Béal, Rémila, & Solal, 2010; Kóczy, 2006; Kóczy & Lauw- ers, 2004; Yang, 2010).
2 Let us already indicate distribuitional effects too: the whole may be more than the parts, but if the gains cannot be distributed in a mutually satisfactory way cooperation may break down.
IV.3 Social networks: How do
Hypothesis 12. A (sub)cluster must be connected: Any
other actor must be a friend's friend's … friend.
The expression "social network" is now widely associated with We realise that a cluster may also be successful as a club in Web 2.0 sites and especially social networking sites. When we helping actors to new acquaintances this being possibly the think of social networks and business we tend to associate to most direct way to obtain more than the parts put together. new websites – the development of the world wide web into We do not want to underplay the importance of new friend- this direction has very quickly dominated the original concept ships, but due to their uncertainty (we do not know who will be of social networks. While today we tend to see social networks our next friend, even), the companies' decisions in joining one as a way teenagers waste their youth although networking or another cluster cannot be made on the basis of these pos- came way before the social networking sites or even the whole sible connections. Once these possible connections are realised the network of connections must be redrawn.
Networking is to build contacts for a possible future coopera- If Hypothesis 12 is found to be true we must slightly modify the tion. Indeed, a cooperation is only possible if the parties know evaluation of the cluster. Not all subclusters can form, rather: each other. Of course we do not talk about cooperation that is typically most cannot form as most are not connected. We can limited to putting together a product of the parts some cluster still consider our previous model, where the connections are actors produce, but of projects where know-how, experience ignored by simply setting the value of impossible subclusters and business ideas are shared to achieve a better product. The to zero making them unattractive. In other words, actors of underlying social or communication network also determines impossible clusters will never be unsatisfied as a group about the cooperation possibilities for the cluster. Only connected the allocation of profits in a cluster. With this change the very projects are possible: projects where any two participants same approach can be used as when the network of connec- can be connected by a series of acquaintances. It is natural to tions is ignored. extend this idea to clusters and subclusters: if a cluster consists of more than one component that are not connected to each other no joint projects will be possible, so having these compo- nents in a common cluster does not bring additional benefits. Hypothesis testing V Hypothesis
We have stated a dozen hypotheses about the way clusters As a simple example consider the so-called ultimatum game. operate (Hypotheses 1–12). In Section I we have given an This game is about sharing a fixed sum, such as €100. The first extensive overview of the literature of cluster evaluation. One player can propose a division, the second player can either would rightly expect that such an amount of literature will accept or reject this. If the second player accepts, the division answer some of our points. Our approach is, however rather is final and the players get the corresponding sums as payoffs. novel focusing on the individual companies' incentives and If the second player rejects, the players get nothing. A rational decision making mechanisms that are quite different from the second player focussing only on the payoffs should always usual data that are more statistical in nature.
accept the proposal, even if she is only offered €1 as this is still more than nothing. In a laboratory the parties are randomly We have made every effort to answer these questions using matched out of the 12–20 participants so that the first player our expertise in clusters and in game theory, but in the absence cannot be identified (and also the first player does not know of an empirical investigation our conclusions remain just specu- the identity of the second player) and therefore personal ties, lations. In the following, however we outline how the missing reputational issues should not play a role. In practice, however information could be obtained. such an offer is rarely accepted, even offers close to the 50– 50 distribution are sometimes turned down suggesting that second players are willing to incur costs in punishing in what V.1 Fundamentals of decision
they see as a deviant behaviour. Interestingly, a series of ex- periments have found that cultural aspects play a crucial role in determining what an acceptable proposal is: in cultures with a We must, first of all understand if the cluster actors make high degree of self reliance only little transfer is expected, while decisions along the rationality principles we have outlined in in societies where cooperation is essential for survival players the first set of hypotheses (Hypotheses 1–7). This requires a may allow only a smaller share to be kept by the proposer. detailed insight into the decision mechanisms of cluster actors as well as the organisation and code of the cluster. We see two The ultimatum game is, of course, just a simple example, but methods to collect such information. such simple games give us information about the way partici- pants make their decisions. Of course hundreds of experiments Firstly we need to conduct interviews with the cluster actors' have already been conducted, but these experiments typically decision makers and the cluster manager. The interviews would involve undergraduate economics students with fresh memo- follow a formal protocol, and with the help of economic psy- ries of their game theory courses. The main reason for this is chologists the answers would be collected in an indirect way. that research is typically conducted at universities where stu- Direct questions would not necessarily result in answers cor- dents are – thanks to the financial compensation – readily avail- responding to the reality: when asked, whether they make sen- able. The second is that research budgets are always too tight sible, economically well-founded decision mechanisms compa- so that the financial compensation offered in an experiment is nies would be inclined to say yes even if this is not the case just less attractive to businessmen. This of course limits the applica- to draw a better image of themselves. bility of those experimental results to our hypotheses requiring new experiments.
Out second method would draw on the methods of experi- mental economists. We would like to conduct simple laborato- ry experiments to find out the motives of the decision makers. V.2 Profi tability
An economic experiment is conducted in a computer labora- tory consisting of a server and a collection of workstations. While the questionnaires and experiments help us to gain gen- Participants make decisions using this computer interface, and eral information about decision making in clusters, the second depending on the participants' decisions the rules of the game group of data is cluster-specific. Ideally we would like to have determine the individual payoffs. This setup has been intro- a figure for the cluster and all its subclusters that describe its duced relatively recently and it is only the last few years that profitability. This is an enormous amount of information that experimental economics grew into a fully recognised discipline. are not only sensitive data, but most likely this information is One of the reasons might be that the results are often surpris- not at all available. In practice we do not need precise data, we ing, demonstrating that culture and morals.
need the profitability of the different subclusters, as perceived by the potential actors. In other words, we do not need to conduct extensive economic analyses for all the (exponential At last, one may resort to questionnaires and interviews asking number of) subclusters, but only approximate figures, as seen about business partners, although such "soft" information is by the companies. more likely to be imprecise and incomplete and companies are likely to be reluctant to share such valuable information.
We are considering several possible methods to obtain relevant data realising that the cluster actors may or may not be too keen to spend time on such studies, but the details are still V.4 Conclusions on the data
open for further research.
Our aim is to study the micro-level incentives and therefore we need micro-level data. The incentives we uncover determine V.3 Networks
the internal stability of the cluster. The quantity and nature of the data needed for the game-theoretic analysis is therefore At last, for an analysis that takes the social or economic net- quite different from the usual benchmark-based evaluation of work within the cluster into account, we must have information clusters. This does not necessarily mean that we must throw about such links. We see 3 ways to gather such data. Firstly, away single-number parameters. Once we get a deeper under- when trying to obtain the value of subclusters, their actors standing of, for instance, the usual structure of the network of might simply respond that they do not know these people and connections within a cluster, we can simulate similar networks therefore cannot give an estimate of the value or profitability and discover correspondences between the size of the cluster of that cluster. In practice, however, it is unlikely that such in terms of actors, the number of "friends" the average actor detailed information is available, the value of the clusters must has. On the other hand there may be a (negative) correlation be estimated in some other way, which takes us to the other between the number of friends for the average actor and the geographical dispersion of the cluster. Unfortunately, to make use of such, readily available indicators one has to explore the A well-managed cluster is likely to have detailed and well doc- relations with the more detailed data.
umented information about past instances of cooperation as well as past business transactions. It may also have informa- tion on how the various cluster actors got involved, perhaps via other cluster actors. This is "hard" information on business relations and is informative not only about the existence of eco- nomic links, but also the intensity of these links. Conclusion
What does the game theoretic approach contribute to the For policy makers and organisations in some form or other understanding of clusters? In economics game theory has interested in cluster support giving them more clear picture brought a complete renewal beginning in the 1950s. While about the operation and risks of the cluster operation which earlier models focussed on profit maximisation and other – helps to subsidize the clusters' development more effective and otherwise valid – arguments, ignored the obvious fact, namely that the interactions are, after all, driven by the individual actors, players, who will play according to the rules and incentives. We do believe that the game theory can seriously influence the By understanding the incentives of the individuals better we research regarding clusters, networks and other co-operations understand the nature of interactions: in this case the efforts among companies. We must admit that in using our game the- put into the cluster better. oretic approach for real-life clusters might have some practical difficulties might arise. We believe that these difficulties may Our model is not omnipotent. Just as microeconomics must be overcome and the benefit is a model that could show us the use demand and production functions we also need a lot of best way to maximize the outcome of our all investment as a information and game theory cannot tell the prospects of a cooperation. Whether a product is good or bad, or how the economic climate might change in the near future are ques- tions that are beyond our model. But after testing of the hypotheses our model will present the possibility to identify such kind of regularity which will help all the cluster actors (policy makers, cluster managers, cluster actors …) to recognize better and sooner not only the risks regarding cluster operation but the methods how we can reduce these risks as well. We do hope that with the help of the game theory the cluster actors after weighing the opportunities up will be able to make rational decisions.
Our results will be also useful for training cluster managers so that the cluster manager him/herself shall help the operation of the cluster as a real "quizmaster" to reduce the recognizable risks, to initiate new projects, to support the implementation of the projects and last but not least to increase the "value" of the cluster in the actors' eyes.
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Dr Zita Zombori
Dr László Á. Kóczy
She is working now at the Chemical Works of Gedeon Richter Graduated from Cambridge he obtained his PhD at the Catho- Plc. She is responsible for the European Affairs, among others lic University Leuven. Taught at Maastricht and Óbuda Universi- for the transnational cooperation aiming to strengthen Rich- ties, currently he is leading the Game Theory Research Group ter's position as innovation leader. Between 2008 and 2010 she at the Research Centre for Economic and Regional Sciences, headed the Hungarian Pole Program Office. The Program aimed Hungarian Academy of Sciences, supported by the prestigeous to create a favourable business environment in the regional Momentum Programme. He is a specialist in theoretical and capitals in addition to the Hungarian Cluster Initiative. Before applied game theory, especially cooperative games with exter- joining the Pole Program Office she held various positions in nalities, industrial organization, social choice and scientomet- the Ministry of Local Government and Regional Development, rics. He published over 15 academic papers attracting over 100 the National Development Agency and at an intermediary body for Structural Funds resources. She has an established track- record of 15 years at the Hungarian Privatization and State Holding Company and at its predecessors. Her main projects included privatization and stock and bond issue processes of major Hungarian companies in the oil and gas, telecommunica- tion, logistics and pharmaceutical sector among others. She is a member of the TACTICS Reflection Group and she is involved in several European projects as well. She is also acting as a key expert to Polish Working Group on Cluster Policy. She is designated member of German Cluster Excellence Initiative's Advisory Board "go-cluster".
Endre Gedai
He is "Integrator", graduate engineer, expert of companies and of companies' cooperation. His practical experience in corporate finance had been acquired between 1990 and 1994 in bank financing and from 1994 to 1998 as managing director of a venture capital company. From 1998 he had been acting as deputy managing director at the Hungarian Privatization and State Holding Company and as a member of more Boards and Supervisory Boards he had got practical experience in corporate management. From 2007 as colleague of the Hungarian Pole Program Office he has been dealing with the theoretical and practical research of clusters and he had taken part in the elaboration of the Hungarian clus- ter development model.    The Institute for Innovation and Technology (iit) covers the entire innovation spectrum on a national and transnational level. Its fundamental elements are the provision of assistance, analysis, evaluation, moderation and the accompaniment of innovative systems and clusters. Its departments provide the basis for these services and are as follows: Innovation Systems and Clusters, Innovation Support, Predicting Success of Collaborate R&D Projects, Safety and Security Systems, Innovation Life Sciences, Evaluation in the area of technology and innovation policy as well as Technical Education and Training. More than 70 scientific employees are part of the team and contribute their technological and socio-economic expertise to project management. Their competencies range from diverse natural sciences, engineering and social sciences to economics. Countries all over the world look for ways to increase their competitiveness. The contribution of cooperating companies in the form of clusters is rather substantial and therefore, for example, the European Union and its member states have long been supporting these cooperative efforts. This support may take the form of a more entrepreneur-friendly legal environment, initiate cooperation, but it may also mean non-returnable financial contribution.
This paper introduces an entirely novel way to study clusters by looking at the selfish, profit-seeking interests of the entrepreneurs, the actors of clusters. The approach, using game theory provides an exact, mathematical framework to study the conflict between the fruitful cooperation represented by the cluster and the selfish ways of the actors to follow their own – possibly short term – interests. The game theoretic approach makes it possible to identify not only good or bad clusters, provide recipes for solutions in some of the bad clusters, but also to define golden rules that do not only facilitate the evaluation of existing clusters, but help future cluster managers to create better, more stable clusters.
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