Reference-Dependent Weak Dominance in 2×2 Coordination Games

Abstract

In this paper we consider 2x2 coordination games with multiple equilibria where pay-offs are measured in an unit of a resource (instead of utilities). The reference point for such games is the pair of max-min payoffs. Each pay-off matrix is associated to two other matrices, one enumerating gains with respect to the max-min pay-off and the other enumerating losses with respect to the max-min pay-off. We prove two propositions about the existence of optimistically weakly dominant action and pessimistically weakly dominant action. The coordination problems are resolved by considering the weakly dominant action for each of the four matrices. In the case of chicken, the “wise outcome” can be attained by incorporating inequality aversion.