Robust models for Nash equilibrium

• Autores: Takashi Matsuhisa
• Localización: Abstracts of the Fifth Spanish Meeting on Game Theory and Applications / coord. por Jesús Mario Bilbao Arrese , Francisco Ramón Fernández García , 2002, ISBN 84-472-0733-1, pág. 120
• Idioma: inglés
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• Resumen

  • This paper investigates the class of the robust models for a mixed strategy Nash equilibrium of a finite strategic form game G.

    The concept of Nash equilibrium has become central in game theory, economics and its related fields. R. J. Aumann and A. Brandenburger (1995, Econometrica 63, 1161�1180) gives epistemic conditions for Nash equilibrium in the model for the modal logic S5. However it is still not yet clear just what classes of models leading to a Nash equilibrium in the epistemic point of view.

    The purposes in this paper are two points: First to introduce the notion of robustness of the S4 logic models for a mixed strategy Nash equilibrium in the game, and secondly to characterize the class R(G) of the robust models as the class E(G) of all the S4 logic models satisfying with common-knowledge of conjectures about the other players� actions. Then we show:

    Theorem 1. The class E(G) is a non-empty subclass of R(G). Furthermore E(G) almost coincides with R(G).