For any given set-valued solution concept, it is possible to consider iterative elimination of actions outside the solution set. This paper applies it 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. Journal of Economic Literature Classification Numbers: C72, C73, D82.

Key Words: equilibrium selection; robustness; incomplete information; perfect foresight dynamics; iteration; monotone potential; p-dominance.

Journal of Economic Theory 144 (2009), 1726-1769. PDF file
First draft: December 31, 2004; this version: January 22, 2009. PDF file
Older version: August 16, 2006. PDF file