Iterated exclusion of implausible types in signaling games

Abstract

Cho and Kreps (1987) proposed a series of criteria for selecting equilibria in signaling games. Their procedure for applying each criterion was to identify all implausible sender types associated with a given off-path message, then look for sequential equilibria assigning probability zero to every implausible type. This paper provides a systematic study of iterated applications of Cho and Kreps (1987) criteria—where in each round, one excludes the additional types that become implausible because given the previously excluded types—, some of which have been proposed in different forms in the literature. Importantly, we show that the iterated exclusion of implausible types selects the same equilibria independently of the exclusion order, and, as a result, it is stronger yet more flexible and often easier to implement than the corresponding criterion. We prove that sequentially stable outcomes (Dilmé, 2024), which exist in all finite signaling games, pass all iterated exclusion procedures.