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Existence of Pure Strategies Nash Equilibria in Social Interaction Games with Dyadic Externalities

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Author Info
Le Breton, Michel
Weber, Shlomo
Abstract

In this note we introduce a general class of games where the payoff of every player are affected by her intrinsic taste for available strategic choices; intensity of her dyadic social interactions of with others in the peer group; and conformity effect. We show, that if the dyadic social influences are symmetric and the conformity effect is identical for all players, every game in our class admits a Nash equilibrium in pure strategies. Our proof relies on the fact that our game is potential (Rosenthal (1973), Monderer and Shapley (1996)). We also illustrate the universality of our result through a large spectrum of applications in economics, political science and sociology.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 7279.

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Date of creation: Apr 2009
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Handle: RePEc:cpr:ceprdp:7279

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Related research
Keywords: conformity effect; dyadic externalities; Nash equilibria; potential games; Social interactions;

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

This paper has been announced in the following NEP Reports:

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  1. Gary S. Becker, 1974. "A Theory of Social Interactions," NBER Working Papers 0042, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  2. Charles F. Manski, 2000. "Economic Analysis of Social Interactions," Journal of Economic Perspectives, American Economic Association, vol. 14(3), pages 115-136, Summer. [Downloadable!] (restricted)
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  3. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September. [Downloadable!] (restricted)
  4. Glaeser, Edward L & Sacerdote, Bruce & Scheinkman, Jose A, 1996. "Crime and Social Interactions," The Quarterly Journal of Economics, MIT Press, vol. 111(2), pages 507-48, May. [Downloadable!] (restricted)
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  5. Bayer, Patrick & Timmins, Christopher, 2005. "On the equilibrium properties of locational sorting models," Journal of Urban Economics, Elsevier, vol. 57(3), pages 462-477, May. [Downloadable!] (restricted)
  6. E. Glaeser & B. Sacerdote & Jose A. Scheinkman, 2003. "The Social Multiplier," Levine's Bibliography 506439000000000130, UCLA Department of Economics. [Downloadable!]
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  7. Nikolai Kukushkin, 2007. "Congestion games revisited," International Journal of Game Theory, Springer, vol. 36(1), pages 57-83, September. [Downloadable!] (restricted)
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  8. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March. [Downloadable!] (restricted)
  9. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February. [Downloadable!] (restricted)
  10. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
  11. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics. [Downloadable!]
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  12. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July. [Downloadable!] (restricted)
  13. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October. [Downloadable!] (restricted)
  14. Fafchamps, Marcel & Gubert, Flore, 2007. "The formation of risk sharing networks," Journal of Development Economics, Elsevier, vol. 83(2), pages 326-350, July. [Downloadable!] (restricted)
  15. Brock, William A & Durlauf, Steven N, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Blackwell Publishing, vol. 68(2), pages 235-60, April.
  16. R. Luce & Albert Perry, 1949. "A method of matrix analysis of group structure," Psychometrika, Springer, vol. 14(2), pages 95-116, June. [Downloadable!] (restricted)
  17. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, vol. 72(1), pages 225-237, January. [Downloadable!] (restricted)
  18. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)
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