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

On Equilibrium in Pure Strategies in Games with Many Players

  • Edward Cartwright

    (Department of Economics, University of Warwick, UK)

  • Myrna Wooders

    (Department of Economics, University of Warwick, UK)

Motivated by issues of imitation, learning and evolution, we introduce a framework of non-co-operative games, allowing both countable sets of pure actions and player types and player types and demonstrate that for all games with sufficiently many players, every mixed strategy Nash equilibrium can be used to construct a Nash e-equilibrium in pure strategies that is 'e-equivalent'. Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functions and any other attributes that are not directly relevant to other players). The set of crowding attributes is assumed to be compact; this is not required, however, for taste attributes. We stress that for studying issues such as conformity, the case of a finite set of types and actions, while illuminating, cannot yield completely satisfactory results. Our main theorems are based on a new mathematical result, in the spirit of the Shapley-Folkman Theorem but applicable to a countable (not necessarily finite dimensional) strategy space.

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://www.feem.it/userfiles/attach/Publication/NDL2003/NDL2003-122.pdf
Download Restriction: no

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2003.122.

as
in new window

Length:
Date of creation: Dec 2003
Date of revision:
Handle: RePEc:fem:femwpa:2003.122
Contact details of provider: Postal: Corso Magenta, 63 - 20123 Milan
Phone: 0039-2-52036934
Fax: 0039-2-52036946
Web page: http://www.feem.it/
Email:


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. Kovalenkov, Alexander & Wooders, Myrna, 2003. "Approximate cores of games and economies with clubs," Journal of Economic Theory, Elsevier, vol. 110(1), pages 87-120, May.
  2. 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.
  3. Theo Offerman & Jan Potters & Joep Sonnemans, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Oxford University Press, vol. 69(4), pages 973-997.
  4. Wooders, Myrna & Edward Cartwright & Selten, Reinhard, 2002. "Social Conformity And Equilibrium In Pure Strategies In Games With Many Players," The Warwick Economics Research Paper Series (TWERPS) 636, University of Warwick, Department of Economics.
  5. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Edward Cartwright & Myrna Wooders, 2003. "On Equilibrium in Pure Strategies in Games with Many Players," Working Papers 2003.122, Fondazione Eni Enrico Mattei.
  7. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
  8. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
  9. Cartwright, Edward & Wooders, Myrna, 2003. "Conformity and Bounded Rationality in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 687, University of Warwick, Department of Economics.
  10. Ehud Kalai, 2001. "Ex-Post Stability in Large Games," Discussion Papers 1351, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Conley, John P. & Wooders, Myrna H., 2001. "Tiebout Economies with Differential Genetic Types and Endogenously Chosen Crowding Characteristics," Journal of Economic Theory, Elsevier, vol. 98(2), pages 261-294, June.
  12. Guilherme Carmona, 2003. "On the Purification of Nash Equilibria of Large Games," Game Theory and Information 0311007, EconWPA.
  13. Edward Cartwright & Myrna Wooders, 2009. "On purification of equilibrium in Bayesian games and expost Nash equilibrium," International Journal of Game Theory, Springer, vol. 38(1), pages 127-136, March.
  14. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
  15. 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.
  16. Conley, John P. & Wooders, Myrna, 1996. "Taste-homogeneity of optimal jurisdictions in a Tiebout economy with crowding types and endogenous educational investment choices," Ricerche Economiche, Elsevier, vol. 50(4), pages 367-387, December.
  17. Martin W. Cripps & Godfrey Keller & Sven Rady, 2002. "Strategic Experimentation: The Case of Poisson Bandits," CESifo Working Paper Series 737, CESifo Group Munich.
  18. 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.
  19. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
  20. Conley, John P. & Wooders, Myrna H., 1997. "Equivalence of the Core and Competitive Equilibrium in a Tiebout Economy with Crowding Types," Journal of Urban Economics, Elsevier, vol. 41(3), pages 421-440, May.
  21. 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.
  22. 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.
  23. 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.
  24. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer, vol. 27(1), pages 83-92.
  25. Pascoa Mario Rui, 1993. "Noncooperative Equilibrium and Chamberlinian Monopolistic Competition," Journal of Economic Theory, Elsevier, vol. 60(2), pages 335-353, August.
  26. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457 Elsevier.
  27. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
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:fem:femwpa:2003.122. 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: (barbara racah)

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.