Social Conformity And Equilibrium In Pure Strategies In Games With Many Players

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Social Conformity And Equilibrium In Pure Strategies In Games With Many Players

Author Info

Wooders, Myrna (Department of Economics, University of Warwick)
Edward Cartwright (Department of Economics, University of Warwick)
Selten, Reinhard (Department of Economics, University of Bonn)

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Abstract

We introduce a framework of noncooperative pregames, in which players are characterized by their attributes, and demonstrate that for all games with sufficiently many players, there exist approximate (e) Nash equilibria in pure strategies. In fact, every mixed strategy equilibrium can be used to construct an e-equilibrium in pure strategies, an ‘e-purification’ result. Our main result is a social conformity theorem. Interpret a set of players, all with attributes in some convex subset of attribute space and all playing the same strategy, as a society. Observe that the number of societies may be as large as the number of players. Our social conformity result dictates that, given e > 0, there is an integer L, depending on e but not on the number of players, such that any sufficiently large game has an e-equilibrium in pure strategies that induces a partition of the player set into fewer than L societies.

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Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 636.

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Length: 59 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:wrk:warwec:636

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Other versions:
- Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2003. "Social Conformity in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 682, University of Warwick, Department of Economics. [Downloadable!]
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Edward Cartwright & Myrna Wooders, 2005. "On Equilibrium in Pure Strategies in Games with Many Players," Working Papers 0511, Department of Economics, Vanderbilt University. [Downloadable!]
Other versions:
- Edward Cartwright & Myrna Wooders, 2003. "On Equilibrium in Pure Strategies in Games with Many Players," Working Papers 2003.122, Fondazione Eni Enrico Mattei. [Downloadable!]
- Cartwright, Edward & Wooders, Myrna, 2003. "On Equilibrium in Pure Stategies in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 686, University of Warwick, Department of Economics. [Downloadable!]
- Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer, vol. 38(1), pages 137-153, March. [Downloadable!] (restricted)
Edward Cartwright, 2004. "Learning to Play Approximate Nash Equilibria in Games with Many Players," Working Papers 2004.85, Fondazione Eni Enrico Mattei. [Downloadable!]
Other versions:
- Cartwright, Edward, 2003. "Learning To Play Approximate Nash Equilibria In Games With Many Players," The Warwick Economics Research Paper Series (TWERPS) 671, University of Warwick, Department of Economics. [Downloadable!]
- Edward Cartwright, 2002. "Learning to play approximate Nash equilibria in games with many players," Levine's Working Paper Archive 506439000000000070, David K. Levine. [Downloadable!]
Edward Cartwright & Myrna Wooders, 2005. "Correlated Equilibrium and Behavioral Conformity," Working Papers 0526, Department of Economics, Vanderbilt University. [Downloadable!]
Other versions:
- Cartwright, Edward & Wooders, Myrna, 2005. "Correlated equilibrium and behavioural conformity," The Warwick Economics Research Paper Series (TWERPS) 732, University of Warwick, Department of Economics. [Downloadable!]
Edward Cartwright & Myrna Wooders, 2003. "Social Conformity and Bounded Rationality in Arbitrary Games with Incomplete Information: Some First Results," Working Papers 2003.119, Fondazione Eni Enrico Mattei. [Downloadable!]
Other versions:
- Cartwright, Edward & Wooders, Myrna, 2003. "Social Conformity And Bounded Rationality In Arbitrary Games With Incomplete Information : Some First Results," The Warwick Economics Research Paper Series (TWERPS) 672, University of Warwick, Department of Economics. [Downloadable!]

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