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 [A. Kajii, S. Morris, The robustness of equilibria to incomplete information, Econometrica 65 (1997) 1283-1309] and absorbing and globally accessible under perfect foresight dynamics for a small friction [A. Matsui, K. Matsuyama, An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415-434]. Several simple sufficient conditions under which a game has an iterated MP-maximizer are also provided.
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Daisuke Oyama, Olivier Tercieux. Iterated potential and robustness of equilibria. Journal of Economic Theory, Elsevier, 2009, 144 (4), pp.1726-1769. ⟨10.1016/j.jet.2009.03.001⟩. ⟨halshs-00754349⟩

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