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Social Networks

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Handbook of Dynamic Game Theory

Abstract

In this chapter, some applications of game theory in social network analysis are presented. We first focus on the opinion dynamics of a social network. Viewing the individuals as players of a game with appropriately defined action (opinion) sets and utility functions, we investigate the best response dynamics and its variants for the game, which would in effect represent the evolution of the individuals’ opinions within a social network. The action sets are defined according to the nature of the opinions, which may be continuous, as for the political beliefs of the individuals, or discrete, as for the type of technology adopted by the individuals to use in their daily lives. The utility functions, on the other hand, are to best capture the social behavior of the individuals such as conformity and stubbornness. For every formulation of the game, we characterize the formation of the opinions as time grows. In particular, we determine whether an agreement among all of the individuals is reached, a clustering of opinions occurs, or none of the said cases happens. We further investigate the Nash equilibria of the game and make clear if the game dynamics converges to one of the Nash equilibria. The rate of convergence to the equilibrium, if it is the case, is also obtained. We then turn our attention to decision-making processes (elections) in social networks, where a collective decision (social choice) must be made by multiple individuals (voters) with different preferences over the alternatives (candidates). We argue that the nonexistence of a perfectly fair social choice function that takes all voter preferences into account leads to the emergence of various strategic games in decision-making processes, most notably strategic voting, strategic candidacy, and coalition formation. While the strategic voting would be played among the voters, the other two games would be played among the candidates. We explicitly discuss the games of strategic candidacy and coalition formation.

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Notes

  1. 1.

    This definition of coordination games is specific to this chapter and may be different from other definitions used in the literature.

References

  • Acemoğlu D, Como G, Fagnani F, Ozdaglar A (2013) Opinion fluctuations and disagreement in social networks. Math Oper Res 38(1):1–27

    Google Scholar 

  • Arrow KJ (1951, 2nd ed., 1963) Social choice and individual values. Yale University Press, New Haven/London

    Google Scholar 

  • Bernard J (1954) The theory of games of strategy as a modern sociology of conflict. Am J Sociol 59(5):411–424

    Google Scholar 

  • Brill M, Conitzer V (2015) Strategic voting and strategic candidacy. AAAI 15:819–826

    Google Scholar 

  • Caplow T (1968) Two against one: coalitions in triads. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Chatterjee S, Seneta E (1977) Towards consensus: some convergence theorems on repeated averaging. J Appl Probab 14(1):89–97

    Google Scholar 

  • Couzin ID, Krause J, Franks NR, Levin SA (2005) Effective leadership and decision-making in animal groups on the move. Nature 433(7025):513–516

    Google Scholar 

  • Cucker F, Smale S (2007) Emergent behavior in flocks. IEEE Trans Autom Control 52(5):852–862

    Google Scholar 

  • Cucker F, Smale S, Zhou D-X (2004) Modeling language evolution. Found Comput Math 4(3):315–343

    Google Scholar 

  • De Sinopoli F (2000) Sophisticated voting and equilibrium refinements under plurality rule. Soc Choice Welf 17(4):655–672

    Google Scholar 

  • Deffuant G, Neau D, Amblard F, Weisbuch G (2000) Mixing beliefs among interacting agents. Adv Complex Syst 3(01n04):87–98

    Google Scholar 

  • DeGroot MH (1974) Reaching a consensus. J Am Stat Assoc 69(345):118–121

    Google Scholar 

  • Dhillon A, Peralta S (2002) Economic theories of voter turnout. Econ J 112(480):332–352

    Google Scholar 

  • Dutta B, Jackson MO, Le Breton M (2001) Strategic candidacy and voting procedures. Econometrica 69(4):1013–1037

    Google Scholar 

  • El Chamie M, Liu J, Başar T (2016) Design and analysis of distributed averaging with quantized communication. IEEE Trans Autom Control 61(12):3870–3884

    Google Scholar 

  • Ellison G (1993) Learning, local interaction, and coordination. Econometrica J Econ Soc 61:1047–1071

    Google Scholar 

  • Ermentrout GB (1992) Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators. SIAM J Appl Math 52(6):1665–1687

    Google Scholar 

  • Etesami SR, Başar T (2015) Game-theoretic analysis of the Hegselmann-Krause model for opinion dynamics in finite dimensions. IEEE Trans Autom Control 60(7):1886–1897

    Google Scholar 

  • Etesami SR, Başar T (2016) Complexity of equilibrium in competitive diffusion games on social networks. Automatica 68:100–110

    Google Scholar 

  • Feddersen TJ, Pesendorfer W (1996) The swing voter’s curse. Am Econ Rev 86:408–424

    Google Scholar 

  • Flierl G, Grünbaum D, Levins S, Olson D (1999) From individuals to aggregations: the interplay between behavior and physics. J Theor Biol 196(4):397–454

    Google Scholar 

  • Gamson WA (1961) A theory of coalition formation. Am Sociol Rev 26:373–382

    Google Scholar 

  • Ghaderi J, Srikant R (2013) Opinion dynamics in social networks: a local interaction game with stubborn agents. In: American control conference (ACC). IEEE, pp 1982–1987

    Google Scholar 

  • Goyal S, Heidari H, Kearns M (2014) Competitive contagion in networks. Games Econ Behav. Online 5 Oct 2014

    Google Scholar 

  • Graver J, Servatius H, Servatius B (1984) Chemical oscillators, waves, and turbulance. Springer, Berlin

    Google Scholar 

  • Harary F (1962) The maximum connectivity of a graph. Proc Natl Acad Sci 48(7):1142–1146

    Google Scholar 

  • Harsanyi JC, Selten R et al (1988) A general theory of equilibrium selection in games, vol 1. MIT Press, Cambridge

    Google Scholar 

  • Hegselmann R, Krause U (2002) Opinion dynamics and bounded confidence models, analysis, and simulation. J Artif Soc Soc Simul 5(3):1–33

    Google Scholar 

  • Huang M, Manton JH (2009) Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior. SIAM J Control Optim 48(1):134–161

    Google Scholar 

  • Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001

    Google Scholar 

  • James S, Lahti T (2006) A theory of participation in elections. Am Econ Rev 96(4):1271–1282

    Google Scholar 

  • Kandori M, Mailath GJ, Rob R (1993) Learning, mutation, and long run equilibria in games. Econometrica J Econ Soc 61:29–56

    Google Scholar 

  • Karp R, Schindelhauer C, Shenker S, Vocking B (2000) Randomized rumor spreading. In: Proceedings of 41st annual symposium on foundations of computer science, pp 565–574

    Google Scholar 

  • Kashyap A, Başar T, Srikant R (2007) Quantized consensus. Automatica 43(7):1192–1203

    Google Scholar 

  • Kempe D, Kleinberg J (2002) Protocols and impossibility results for gossip-based communication mechanisms. In: Proceedings of 43rd annual IEEE symposium on foundations of computer science, pp 471–480

    Google Scholar 

  • Ledyard JO et al (1981) The paradox of voting and candidate competition: a general equilibrium analysis. Technical report

    Google Scholar 

  • Lin P, Jia Y (2009) Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies. Automatica 45(9):2154–2158

    Google Scholar 

  • Lorenz J, Urbig D (2007) About the power to enforce and prevent consensus by manipulating communication rules. Adv Complex Syst 10(02):251–269

    Google Scholar 

  • Lynch NA (1996) Distributed algorithms. Morgan Kaufmann, San Francisco

    Google Scholar 

  • Marden JR, Arslan G, Shamma JS (2009) Cooperative control and potential games. IEEE Trans Syst Man Cybern B Cybern 39(6):1393–1407

    Google Scholar 

  • Montanari A, Saberi A (2009) Convergence to equilibrium in local interaction games. In: 50th annual IEEE symposium on foundations of computer science, FOCS’09. IEEE, pp 303–312

    Google Scholar 

  • Muller E, Satterthwaite MA (1977) The equivalence of strong positive association and strategy-proofness. J Econ Theory 14(2):412–418

    Google Scholar 

  • Myerson RB, Weber RJ (1993) A theory of voting equilibria. Am Polit Sci Rev 87(1):102–114

    Google Scholar 

  • Nedić A, Olshevsky A, Ozdaglar A, Tsitsiklis JN (2009) On distributed averaging algorithms and quantization effects. IEEE Trans Autom Control 54(11):2506–2517

    Google Scholar 

  • Palfrey TR, Rosenthal H (1985) Voter participation and strategic uncertainty. Am Polit Sci Rev 79(1):62–78

    Google Scholar 

  • Shenoy PP (1978) On coalition formation in simple games: a mathematical analysis of Caplow’s and Gamson’s theories. J Math Psychol 18(2):177–194

    Google Scholar 

  • Strogatz SH (2001) Exploring complex networks. Nature 410(6825):268–276

    Google Scholar 

  • Sun YG, Wang L (2009) Consensus of multi-agent systems in directed networks with nonuniform time-varying delays. IEEE Trans Autom Control 54(7):1607–1613

    Google Scholar 

  • Swedberg R (2001) Sociology and game theory: contemporary and historical perspectives. Theory Soc 30(3):301–335

    Google Scholar 

  • Tsitsiklis JN (1984) Problems in decentralized decision making and computation. Technical report, DTIC Document

    Google Scholar 

  • Weisbuch G, Deffuant G, Amblard F, Nadal J-P (2002) Meet, discuss, and segregate! Complexity 7(3):55–63

    Article  Google Scholar 

  • Young HP (2001) Individual strategy and social structure: an evolutionary theory of institutions. Princeton University Press, Princeton

    Google Scholar 

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Author information

Authors and Affiliations

  1. Coordinated Science Laboratory, University of Illinois, 61801, Urbana-Champaign, Urbana, IL, USA

    Sadegh Bolouki

  2. School of ECEE, Arizona State University, 85287, Tempe, AZ, USA

    Angelia Nedić

  3. Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Tamer Başar

Authors
  1. Sadegh Bolouki
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  2. Angelia Nedić
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  3. Tamer Başar
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Corresponding author

Correspondence to Sadegh Bolouki .

Editor information

Editors and Affiliations

  1. Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

    Tamer Başar

  2. Department of Decision Sciences GERAD, HEC Montréal, Montreal, Québec, Canada

    Georges Zaccour

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Bolouki, S., Nedić, A., Başar, T. (2018). Social Networks. In: Başar, T., Zaccour, G. (eds) Handbook of Dynamic Game Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-44374-4_32

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