Convex Approximation of Bounded Rational Equilibria

In this paper, we consider the existence of a sequence of convex sets that has an approximation property for the equilibrium sets in the bounded rational environments. We show that the bounded rational equilibrium multivalued map is approximated with arbitrary precision in the abstract framework, a parameterized class of "general games" together with an associated abstract rationality function that is established by Anderlini and Canning (2001). As an application, we show that the existence of a selection for some bounded rational equilibria on a discontinuous region P when P is a perfect set.