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. Journal of Economic Literature Classification Numbers: C72, C73, D82.

Population Games and Deterministic Evolutionary Dynamics

“…The use of a fixed sample size is not essential: the same result holds so long as enough probability is placed on sample sizes no greater than k. Moreover, the selection result extends to iterated versions of p-dominance (Tercieux, 2006;Oyama and Tercieux, 2009), as we illustrate through an example. The use of a fixed sample size is not essential: the same result holds so long as enough probability is placed on sample sizes no greater than k. Moreover, the selection result extends to iterated versions of p-dominance (Tercieux, 2006;Oyama and Tercieux, 2009), as we illustrate through an example.…”

Iterated generalized half-dominance and global game selection

“…6 Their result is generalized by subsequent papers including Sorger (1999, 2002), Oyama (2002), Tercieux (2006), Kojima (2006), and Oyama et al (2008). In particular, Oyama and Tercieux (2009) show that iterated p-dominance with i p i < 1 is selected by perfect foresight dynamics. stochastic length of time.…”

“…, 1) in Example 2 is not a p-dominant equilibrium with i p i < 1 if n is not small. In fact, it is also not an iterated p-dominant equilibrium with i p i < 1 (Oyama and Tercieux, 2009). 9 Note, however, that a GH-dominant equilibrium is a (1/2, .…”

“…Their proof is based on a version of the critical path lemma (Kajii and Morris, 1997). Oyama and Tercieux (2009) show that an iterated p-dominant equilibrium with i p i < 1 is selected. Their proof uses a form of generalized potential function with supermodularity, which extends the result by Oyama et al (2008).…”

Generalized Belief Operator and Robustness in Binary‐Action Supermodular Games

“… For further developments in the literature see, for example, Oyama and Tercieux (), Nora and Uno (), and Haimanko and Kajii (). …”