Barlo, Mehmet and Carmona, Guilherme (2011): Strategic behavior in non-atomic games.
Download (271kB) | Preview
In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player's belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.
|Item Type:||MPRA Paper|
|Original Title:||Strategic behavior in non-atomic games|
|Keywords:||Strategic equilibrium; Games with a continuum of players; Equilibrium distributions|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games|
|Depositing User:||Mehmet Barlo|
|Date Deposited:||23. Dec 2011 16:09|
|Last Modified:||15. Feb 2013 19:40|
Aumann, R., and A. Brandenburger (1995): "Epistemic Conditions for Nash Equilibrium," Econometrica, 63, 1161- 1180.
Barlo, M. (2003): "Essays in Game Theory," Ph.D. thesis, University of Minnesota.
Carmona, G. (2008): "Large Games with Countable Characteristics," Journal of Mathematical Economics, 44, 344-347.
Carmona, G. (2009): "A Remark on the Measurability of Large Games," Economic Theory, 39, 41-44.
Carmona, G., and K. Podczeck (2009): "On the Existence of Pure Strategy Nash Equilibria in Large Games," Journal of Economic Theory, 144, 1300-1319.
Carmona, G., and K. Podczeck (2011): "Approximation and Characterization of Nash Equilibria of Large Games," University of Cambridge and Universitat Wien.
Chari, V. V., and P. J. Kehoe (1989): "Sustainable Plans," Journal of Political Economy, 98(4), 783-802.
Green, E. (1980): "Non-Cooperative Price Taking in Large Dynamic Markets," Journal of Economic Theory, 22, 155-182.
Hildenbrand, W. (1974): Core and Equilibria of a Large Economy. Princeton University Press, Princeton.
Khan, M., K. Rath, and Y. Sun (1997): "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, 76, 13-46.
Khan, M., and Y. Sun (1995): "The Marriage Lemma and Large Anonymous Games with Countable Actions," Mathematical Proceedings of the Cambridge Philosophical Society, 117, 385-387.
Kuhn, H. e. a. (1996): "The Work of John Nash in Game Theory," Journal of Economic Theory, 69, 153-185.
Levine, D., and W. Pesendorfer (1995): "When Are Agents Negligible?," American Economic Review, 85(5), 1160-1170.
Mas-Colell, A. (1984): "On a Theorem by Schmeidler," Journal of Mathematical Economics, 13, 201-206.
Nash, J. (1950): "Non-Cooperative Games," Ph.D. thesis, Princeton University.
Parthasarathy, K. (1967): Probability Measures on Metric Spaces. Academic Press, New York.
Podczeck, K. (2008): "On the Convexity and Compactness of the Integral of a Banach Space Valued Correspondence," Journal of Mathematical Economics, 44, 836-852.
Sabourian, H. (1990): "Anonymous Repeated Games with a Large Number of Players and Random Outcomes," Journal of Economic Theory, 51, 92-110.
Selten, R. (1975): "Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games," International Journal of Game Theory, 4, 25-55.