Iterated Potential and Robustness of Equilibria

Oyama, Daisuke and Tercieux, Olivier (2004): Iterated Potential and Robustness of Equilibria.

Abstract

For any given set-valued solution concept, it is possible to consider iterative elimination of actions outside the solution set. This paper applies such a procedure to define the concept of iterated monotone potential maximizer (iterated MP-maximizer). It is shown that under some monotonicity conditions, an iterated MP-maximizer is robust to incomplete information (Kajii and Morris, Econometrica 65 (1997)) and absorbing and globally accessible under perfect foresight dynamics for a small friction (Matsui and Matsuyama, Journal of Economic Theory 65 (1995)). Several simple sufficient conditions under which a game has an iterated MP-maximizer are also provided.

• Item Type: MPRA Paper
• Language: English
• Keywords: equilibrium selection; robustness; incomplete information; perfect foresight dynamics; iteration; monotone potential; p-dominance
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

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