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Some First Results for Noncooperative Pregames : Social Conformity and Equilibrium in Pure Strategies

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  • Wooders, M.
  • Selten, R.
  • Cartwright, E.

Abstract

We introduce the framework of noncooperative pregames and demonstrate that for all games with sufficiently many players, there exists approximate (E) Nash equilibria in pure strategies. Moreover, an equilibrium can be selected with the property that most players choose the same strategies as all other players with similar attributes. More precisely, there is an integer K, depending on E but not on the number of players so that any sufficiently large society can be partitioned into fewer than K groups, or cultures, consisting of similar players, and all players in the same group play the same pure strategy. In ongoing research we are extending the model to cover a broader class of situations, including incomplete information.

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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp589rev.pdf
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Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 589.

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Length: 32 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:wrk:warwec:589

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Keywords: GAMES ; INFORMATION ; STRATEGIC PLANNING;

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References

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  1. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  2. Aloisio Ara�jo & Jaime Orrillo & Mario R. Páscoa, 2000. "Equilibrium with Default and Endogenous Collateral," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 1-21.
  3. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer, vol. 27(1), pages 83-92.
  4. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
  5. Ehud Kalai, 2000. "Private Information in Large Games," Discussion Papers 1312, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  7. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
  8. Kovalenkov, A. & Holtz Wooders, M., 1997. "An Explicit Bound on epsilon for Non-Emptiness of the epsilon-Core of an Arbitrary Game with Side Payments," UFAE and IAE Working Papers 393.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. Myrna Wooders & Alexander Kovalenkov, 2001. "Epsilon cores of games with limited side payments Nonemptiness and equal treatment," Economics Bulletin, AccessEcon, vol. 28(5), pages A0.
  10. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
  11. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-50, November.
  12. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December.
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Cited by:
  1. Carmona, Guilherme, 2004. "Nash and Limit Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series wp442, Universidade Nova de Lisboa, Faculdade de Economia.
  2. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2003. "Social Conformity in Games with Many Players," Working Papers 2003.121, Fondazione Eni Enrico Mattei.
  3. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2005. "Behavioral Conformity in Games with Many Players," Vanderbilt University Department of Economics Working Papers 0513, Vanderbilt University Department of Economics.
  4. Guilherme Carmona, 2004. "Nash Equilibria of Games with a Continuum of Players," Game Theory and Information 0412009, EconWPA.

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