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## Wwwconference.org

**WWW 2011 – Tutorial**
**March 28–April 1, 2011, Hyderabad, India**
**Tutorial: Game Theoretic Models for Social Network**
Ramasuri Narayanam
Electronic Commerce Laboratory
IBM India Research Lab
Dept. of Computer Science and Automation
Indian Institute of Science, Bangalore, India
ten, the individuals in the network exhibit strategic
The existing methods and techniques for social network anal-
ysis are inadequate to capture both the behavior (such asrationality and intelligence) of individuals and the strate-
2. They do not explicitly capture the dynamics of strate-
gic interactions that occur among these individuals. Game
gic interaction among the individual in the networks.

theory is a natural tool to overcome this inadequacy since
Game theory [12, 13] is a natural tool to overcome these
it provides rigorous mathematical models of strategic inter-
fundamental problems, as it provides a rich suite of mathe-
action among autonomous, intelligent, and rational agents.

matical models of strategic interaction among autonomous,
Motivated by the above observation, this tutorial provides
intelligent, and rational individuals (or players). Game the-
the conceptual underpinnings of the use of game theoretic
oretic models are thus best suited to capture the strategic
models in social network analysis. In the ﬁrst part of the tu-
nature of individuals making up a social network. Game
torial, we provide rigorous foundations of relevant concepts
theoretic models are also complementary to the current SNA
in game theory and social network analysis.

approaches and hence they add a new dimension to the area
ond part of the tutorial, we present a comprehensive study
of SNA. Recently there have been several eﬀorts in following
of four contemporary and pertinent problems in social net-
a game theoretic approach to social network modeling [18,
works: social network formation, determining in inﬂuential
7, 5, 10, 15, 6, 11, 9, 2, 1, 17, 16].

individuals for viral marketing, query incentive networks,
In our view, game theoretic models are appropriate for
and community detection.

social network analysis from two perspectives:(a) Game theoretic models are very natural for several prob-

**Categories and Subject Descriptors**
lems in social network analysis. A few such problems include
F.2.2 [

**Analysis of Algorithms and Problem Complex-**
social network formation [7, 5, 10, 15], social network mon-

**ity**]: Nonnumerical Algorithms and Problems

etization [6], and bargaining on networks [11].

(b) Game theoretic models are useful as a tool to solve cer-tain interesting problems in social network analysis. This
leads to not only a deeper understanding of those problems
Economics, Theory
but also eﬃcient algorithms. A few examples of this kindinclude query incentive networks [9, 2], discovering commu-
nities in networks [1, 17], determining inﬂuential individualsfor viral marketing [16], etc.

Social networks, game theory, viral marketing, network for-mation, query incentive networks, community detection

**CONTENT OF THE TUTORIAL**
Here we present a brief description of the material and the
results that we discuss in this tutorial.

Social network analysis (SNA) [19] comprises a well devel-
oped suite of measures and metrics based on techniques such

**Social Network Analysis: A Quick Primer**
as graph theory, spectral theory, optimization theory. Allthis machinery in SNA is useful to measure the structural
First, we present a quick primer on social network analysis
and statistical properties of social networks. In fact, gen-
from Easley and Kleinberg [4]. We deﬁne important metrics
erative models can reproduce networks with similar/same
for social network analysis, prominent approaches for social
structural properties. However, the current SNA approaches
network analysis, and list a few benchmark problems.

are inadequate for the following reasons:

**Foundational Concepts in Game Theory**
1. They do not satisfactorily capture the behavior of the
Here we ﬁrst present the basic concepts from both non-
individuals in social networks. For example, very of-
cooperative game theory and cooperative game theory. Ma-jority of this content is covered from Myerson [12]. We then
Copyright is held by the author/owner(s).

present the foundational principles of mechanism design the-

*WWW 2011, *March 28–April 1, 2011, Hyderabad, India.

ory from Narahari, Garg, Ramasuri, and Hastagiri [13].

**WWW 2011 – Tutorial**
**March 28–April 1, 2011, Hyderabad, India**
**Social Network Formation**
cial network analysis. We then motivate the need for a game
The behavior of networks is driven by the actions of a
theoretic approach to community detection and present two
large number of autonomous individuals, each motivated by
game theoretic models for community detection Chen, Liu,
self-interest and individual objectives. As a consequence of
Sun, and Wang [1] and Ramasuri and Narahari [17].

this, the global performance of such networks, which arethe equilibrium outcomes of decentralized strategic interac-
tions, can be worse than that of a network that is enforced
[1] W. Chen, Z. Liu, X. Sun, and Y. Wang.

*A game*
by a central authority. In the literature, networks that are

*theoretic framework to identify overlapping*
enforced by a central authority are known as eﬃcient net-

*communities in social networks*. DMKD, 21:224-240,
works. Understanding the compatibility between the equi-
librium networks and eﬃcient networks is the primary focus
[2] D. Dikshit and Y. Narahari.

*Truthful and Quality*
of research in network formation. Most of the results that we

*Conscious Query Incentive Networks. *In Workshop on
cover in this context are primarily from Jackson [7], Goyal
Internet and Network Economics (WINE), 2009.

[5], Kleinberg, Suri, Tardos, and Wexler [10], and Ramasuri
[3] P. Domingos and M. Richardson.

*Mining the network*
and Narahari [15].

*value of customers. *In ACM SIGKDD, 2001.

**Discovering Influential Individuals for Vi-**
[4] D. Easley and J. Kleinberg.

*Networks, Crowds, and*
*Markets: Reasoning about a Highly Connected World.*

Cambridge University Press, Cambridge, UK, 2010.

Viral Marketing is based on the conceptual framework of
[5] S. Goyal.

*Connections: An Introduction to the*
diﬀusion of information. In this context, given a integer

*Economics of Networks*. Princeton University Press,
value

*k*, it is very challenging to determine top-

*k *inﬂuential
Princeton and Oxford, 2007.

individuals to maximize the volume of information cascade.

Formally, we deﬁne an objective function

*σ*(

*.*) as follows. We
[6] J.D. Hartline, V.S. Mirrokni, M. Sundararajan.

note that an individual is active if he/she adopts the product

*Optimal marketing strategies over social networks. *In
or technology. If

*S *is the set of initially active nodes, then

*σ*(

*S*) is the expected number of active nodes at the end of the
[7] M. O. Jackson.

*Social and Economic Networks*.

diﬀusion process. For a given constant

*k*, the top-

*k *nodes
Princeton University Press, 2008.

problem seeks to ﬁnd a subset of nodes

*S *of cardinality
[8] D. Kempe, J. Kleinberg, and E. Tardos.

*Maximizing*
*k *that maximizes the value of

*σ*(

*S*). In this setting, we

*the spread of inﬂuence through a social network. *In
ﬁrst cover certain fundamental results from Domingos and
ACM SIGKDD, 2003.

Richardson [3], Kempe, Kleinberg, and Tardos [8]. Then
[9] J.M. Kleinberg and P. Raghavan.

*Query Incentive*
we present a game theoretic approach to address the top-

*k*
*Networks. *In IEEE FOCS, pages 132-141, 2005.

nodes problem and we present a few results from Ramasuri
[10] J. Kleinberg, S. Suri, E. Tardos, and T. Wexler.

and Narahari [16].

*Strategic network formation with structural holes*. InACM EC, pages 284-293, 2008.

**Query Incentive Networks**
[11] J.M. Kleinberg and E. Tardos.

*Balanced outcomes in*
We consider scenarios where a person in a social network

*social exchange networks. *In STOC, 2008.

is seeking some information from the social network and the
[12] R.B. Myerson.

*Game Theory: Analysis of Conﬂict.*
other connected individuals forward the query down in the
Harvard University Press, 1997.

network as well as report back the answer, if any. Since ev-
[13] Y. Narahari, Dinesh Garg, Ramasuri Narayanam,
ery individual is an intelligent and rational agent and since
Hastagiri Prakash.

*Game Theoretic Problems in*
forwarding the query (and then reporting back the answer)

*Network Economics and Mechanism Design Solutions.*
requires a certain amount of eﬀort on her part, she may not
In Series: Advance Information & Knowledge
be willing to do so. While oﬀering an appropriate incen-
Processing (AIKP), Springer Verlag, London, 2009.

tive to the intermediate nodes will increase the total reward
[14] Prabhakar Raghavan and Jon Kleinberg.

*Query*
which must be oﬀered by the person posing the query, it

*Incentive Networks. *In IEEE FOCS, 2005.

will also increase the exposure of the query. This concept
[15] Ramasuri Narayanam and Y. Narahari.

*Topologies of*
was captured by the model of Raghavan and Kleinberg [14]

*Strategically Formed Social Networks Based on a*
who called these

*query incentive networks*. In the tutorial,

*Generic Value Function - Allocation Rule Model. *To
we will bring out the role of game theory and mechanism
appear in Social Networks (Elsevier), 2011.

design in the design of incentives in such networks [14, 2].

[16] Ramasuri Narayanam and Y. Narahari.

*A Shapley*
**Community Detection in Social Networks**
*Value based Approach to Discover Inﬂuential Nodes inSocial Networks. *In IEEE TASE, 8(1):130-147, 2011.

A community structure in a network is a division of net-
[17] Ramasuri Narayanam and Y. Narahari.

*Nash Stable*
work nodes into groups within which the network connec-

*Partitioning of Graphs with Application to Community*
tions are dense, but between which the connections are sparse.

*Detection in Social Networks. *Under Review, 2010.

Detecting communities in networks helps to understand theunderlying characteristics of large networks. We ﬁrst men-
[18] S. Suri.

*The Eﬀects of Network Topology on Strategic*
tion several variants of community detection in networks

*Behavior*. PhD thesis, Dept. of Computer and
such as graph partitioning, ﬁnding the most dense subgraph
Information Science, University of Pennsylvania, 2007.

in a given graph. Next we brieﬂy mention various techniques
[19] S. Wasserman and K. Faust.

*Social Network Analysis*.

for community detection like spectral methods, multi-level
Cambridge University Press, Cambridge, 1994.

methods, optimization methods, and methods based on so-

Source: http://wwwconference.org/proceedings/www2011/companion/p291.pdf

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