Asymptotic interpretations for equilibria of nonatomic games
We 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.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 47 (2011)
Issue (Month): 4-5 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/locate/jmateco|
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.:
- 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.
- 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.
- 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.
- Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, EconWPA.
- Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
- Ehud Kalai, 2004.
"Large Robust Games,"
Econometric Society, vol. 72(6), pages 1631-1665, November.
- Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
- 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.
- 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, 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.
- Balder, Erik J., 2002. "A Unifying Pair of Cournot-Nash Equilibrium Existence Results," Journal of Economic Theory, Elsevier, vol. 102(2), pages 437-470, February.
- Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:491-499. 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: (Shamier, Wendy)
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.