This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Nash and Limit Equilibria of Games with a Continuum of Players

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Carmona, Guilherme

Additional information is available for the following registered author(s):

Abstract

We show that a strategy is a Nash equilibrium in a game with a continuum of players if and only if there exists a sequence of finite games such that its restriction is an "n-equilibria, with "n converging to zero. In our characterization, the sequence of finite games approaches the continuum game in the sense that the set of players and the distribution of characteristics and actions in the finite games converge to those of the continuum game. These results render approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance. Also, they suggest defining a refinement of Nash equilibria for games with a continuum of agents as limit points of equilibria of finite games. This allows us to discard those Nash equilibria that are artifacts of the continuum model, making limit equilibrium a natural equilibrium concept for games with a continuum of players.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. 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://fesrvsd.fe.unl.pt/WPFEUNL/WP2004/wp442.pdf
File Format:
File Function:
Download Restriction: no

Publisher Info
Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp442.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 39 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:unl:unlfep:wp442

Contact details of provider:
Web page: http://www.fe.unl.pt

For technical questions regarding this item, or to correct its listing, contact: (Lourdes Gouveia).

Related research
Keywords: Nash equilibrium; limit equilibrium; noncooperative games; continuum of players;

Other versions of this item:

This paper has been announced in the following NEP Reports: 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.:
  1. Dubey, Pradeep & Mas-Colell, Andreau & Shubik, Martin, 1980. "Efficiency properties of strategies market games: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 22(2), pages 339-362, April. [Downloadable!] (restricted)
  2. Fudenberg, Drew & Levine, David, 1986. "Limit games and limit equilibria," Journal of Economic Theory, Elsevier, vol. 38(2), pages 261-279, April. [Downloadable!] (restricted)
    Other versions:
  3. Hildenbrand, W & Mertens, J F, 1972. "Upper Hemi-Continuity of the Equilibrium-Set Correspondence for Pure Exchange Economies," Econometrica, Econometric Society, vol. 40(1), pages 99-108, January. [Downloadable!] (restricted)
  4. Green, Edward J., 1980. "Noncooperative price taking in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 22(2), pages 155-182, April. [Downloadable!] (restricted)
  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.
    Other versions:
  6. 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.
  7. Postlewaite, A & Schmeidler, David, 1978. "Approximate Efficiency of Non-Walrasian Nash Equilibria," Econometrica, Econometric Society, vol. 46(1), pages 127-35, January. [Downloadable!] (restricted)
  8. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10. [Downloadable!] (restricted)
  9. Hart, Sergiu & Hildenbrand, Werner & Kohlberg, Elon, 1974. "On equilibrium allocations as distributions on the commodity space," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 159-166, August. [Downloadable!] (restricted)
  10. Carmona, Guilherme, 2003. "On the Purification of Nash Equilibria of Large Games," FEUNL Working Paper Series wp436, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
    Other versions:
  11. Green, Edward J, 1984. "Continuum and Finite-Player Noncooperative Models of Competition," Econometrica, Econometric Society, vol. 52(4), pages 975-93, July. [Downloadable!] (restricted)
    Other versions:
  12. Mas-Colell, Andreu, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part I: Mixed strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 153-170, June. [Downloadable!] (restricted)
  13. Bamon, Rodrigo & Fraysse, Jean, 1985. "Existence of Cournot Equilibrium in Large Markets," Econometrica, Econometric Society, vol. 53(3), pages 587-97, May. [Downloadable!] (restricted)
  14. M Ali Khan & Yeneng Sun, 2002. "Non-Cooperative Games with Many Players," Economics Working Paper Archive 482, The Johns Hopkins University,Department of Economics. [Downloadable!]
    Other versions:
  15. Wooders, M. & Selten, R. & Cartwright, E., 2001. "Some First Results for Noncooperative Pregames : Social Conformity and Equilibrium in Pure Strategies," The Warwick Economics Research Paper Series (TWERPS) 589, University of Warwick, Department of Economics. [Downloadable!]
  16. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer, vol. 2(3), pages 427-33, July.
  17. Novshek, William & Sonnenschein, Hugo, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 171-187, June. [Downloadable!] (restricted)
  18. Hildenbrand, Werner, 1970. "On economies with many agents," Journal of Economic Theory, Elsevier, vol. 2(2), pages 161-188, June. [Downloadable!] (restricted)
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.)

  1. Guilherme Carmona, 2003. "Symmetric Approximate Equilibrium Distributions with Finite Support," Game Theory and Information 0311006, EconWPA. [Downloadable!]
    Other versions:
  2. Guilherme Carmona, 2004. "On the Existence of Equilibrium Bank Runs in a Diamond-Dybvig Environment," Finance 0404009, EconWPA. [Downloadable!]
    Other versions:
Statistics
Access and download statistics

Did you know? There is a FAQ (frequently asked questions).

This page was last updated on 2009-11-25.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.