Invariance properties of persistent equilibria and related solution concepts

Kohlberg and Mertens argued that a solution concept to a game should be invariant under the addition of deletion of an equivalent strategy and not require the use of weakly dominated strategies. In this paper we study which of these requirements are satisfied by Kalai and Samet's concepts of persistent equilibria and persistent retracts. While none of these concepts has all the invariance properties, we show that a slight rephrasing of the notion of a persistent retract leads to a notion satisfying them all