Asymptotic interpretations for equilibria of nonatomic games
AbstractWe show that a mixed equilibrium of a semi-anonymous nonatomic game can be used to generate pure-strategy profiles for finite games randomly generated from the type distribution of the nonatomic game. As the numbers of players involved in the finite games increase, the generated profiles will be asymptotically equilibrium. The converse of this result is also true, i.e., a mixed-strategy profile that is not an equilibrium for the nonatomic game will not be able to achieve the above asymptotic rationality for large finite games. The combined finding can be specialized to situations where the nonatomic game is anonymous and where the given equilibrium is pure. Besides their practical values, these results offer yet one more justification for the study of nonatomic games. They also suggest that efforts may be better spent on searching for mixed rather than pure equilibria of nonatomic games.
Download InfoIf 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.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 47 (2011)
Issue (Month): 4-5 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/jmateco
Nonatomic games; Law of large numbers; Empirical distribution;
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.:
- Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
- Guilherme Carmona, 2004.
"Nash Equilibria of Games with a Continuum of Players,"
Game Theory and Information
- Carmona, Guilherme, 2004. "Nash Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series wp466, Universidade Nova de Lisboa, Faculdade de Economia.
- Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
- Al-Najjar, Nabil I., 2008. "Large games and the law of large numbers," Games and Economic Behavior, Elsevier, vol. 64(1), pages 1-34, September.
- Guilherme Carmona, 2003.
"Nash and Limit Equilibria of Games with a Continuum of Players,"
Game Theory and Information
- 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.
- Green, Edward J, 1984.
"Continuum and Finite-Player Noncooperative Models of Competition,"
Econometric Society, vol. 52(4), pages 975-93, July.
- 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.
- Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
- Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
- Ehud Kalai, 2002.
"Large Robust Games,"
1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.