Entropic selection of Nash equilibrium

Alioğulları, Zeynel Harun and Barlo, Mehmet (2012): Entropic selection of Nash equilibrium.

Abstract

This study argues that Nash equilibria with less variations in players' best responses are more appealing. To that regard, a notion measuring such variations, the entropic selection of Nash equilibrium, is presented: For any given Nash equilibrium, we consider the cardinality of the support of a player's best response against others' strategies that are sufficiently close to the behavior specified. These cardinalities across players are then aggregated with a real-valued function on whose form we impose no restrictions apart from the natural limitation to nondecreasingness in order to obtain equilibria with less variations. We prove that the entropic selection of Nash equilibrium is non-empty and admit desirable properties. Some well-known games, each of which display important insights about virtues / problems of various equilibrium notions, are considered; and, in all of these games our notion displays none of the criticisms associated with these examples. These examples also show that our notion does not have any containment relations with other associated and well-known refinements, perfection, properness and persistence.

• Item Type: MPRA Paper
• Language: English
• Keywords: Entropic Selection of Nash Equilibrium; Refinements of Nash Equilibrium
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Aumann, R., and A. Brandenburger (1995): "Epistemic Conditions for Nash Equilibrium," Econometrica, 63, 1161-1180.

Barlo, M., and G. Carmona (2011): "Strategic Behavior in Non-Atomic Games," Sabanci University and University of Cambridge.

Kalai, E., and D. Samet (1984): "Persistent Equilibria in Strategic Games," International Journal of Game Theory, 13, 129-144.

Kohlberg, E., and J.-F. Mertens (1986): "On the Strategic Stability of Equilibria," Econometrica, 54, 1003-1039.

Kuhn, H. e. a. (1996): "The Work of John Nash in Game Theory," Journal of Economic Theory, 69, 153-185.

Myerson, R. B. (1978): "Refiments of the Nash Equilibrium Concept," International Journal of Game Theory, 7, 73-80.

Nash, J. (1950): "Non-Cooperative Games," Ph.D. thesis, Princeton University.

Selten, R. (1975): "Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games," International Journal of Game Theory, 4, 25-55.

Shannon, C. E. (1948): "A Mathematical Theory of Communication," Bell System Technical Journal.