IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

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

  • Wooders, Myrna

    (Department of Economics, University of Warwick)

  • Edward Cartwright

    (Department of Economics, University of Warwick)

  • Selten, Reinhard

    (Department of Economics, University of Bonn)

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp636.pdf
Download Restriction: no

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

as
in new window

Length: 59 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:wrk:warwec:636
Contact details of provider: Postal: CV4 7AL COVENTRY
Phone: +44 (0) 2476 523202
Fax: +44 (0) 2476 523032
Web page: http://www2.warwick.ac.uk/fac/soc/economics/

More information through EDIRC

References listed on IDEAS
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.:

as in new window
  1. Pascoa Mario Rui, 1993. "Noncooperative Equilibrium and Chamberlinian Monopolistic Competition," Journal of Economic Theory, Elsevier, vol. 60(2), pages 335-353, August.
  2. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2003. "Social Conformity in Games with Many Players," Working Papers 2003.121, Fondazione Eni Enrico Mattei.
  3. Binmore, Ken & Samuelson, Larry, 2001. "Evolution and Mixed Strategies," Games and Economic Behavior, Elsevier, vol. 34(2), pages 200-226, February.
  4. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  5. M Ali Khan & Kali P Rath & Yeneng Sun, 1994. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economics Working Paper Archive 381, The Johns Hopkins University,Department of Economics, revised Feb 1997.
  6. Fudenberg, Drew & Ellison, Glenn, 1995. "Word-of-Mouth Communication and Social Learning," Scholarly Articles 3196300, Harvard University Department of Economics.
  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. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  10. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  11. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  12. Gale, D. & Rosental, R.W., 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 65, Boston University - Industry Studies Programme.
  13. 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.
  14. Ehud Kalai, 2000. "Private Information in Large Games," Discussion Papers 1312, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Scharfstein, David S & Stein, Jeremy C, 1990. "Herd Behavior and Investment," American Economic Review, American Economic Association, vol. 80(3), pages 465-79, June.
  16. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
  17. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
  18. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
  19. Green, Edward J., 1982. "Continuum and Finite-Player Noncooperative Models of Competition," Working Papers 418, California Institute of Technology, Division of the Humanities and Social Sciences.
  20. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  21. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  22. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346.
  23. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December.
  24. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
  25. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  26. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
  27. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer, vol. 27(1), pages 83-92.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:wrk:warwec:636. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Helen Neal)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.