On equilibria in constrained generalized games with the weak continuous inclusion property

Abstract

In this paper, we present results that use Himmelberg's fixed point theorem to highlight substantive trade-offs between compactness, continuity and convexity postulates in the setting of a constrained generalized game. The primary contribution is a focus on weakening the compactness assumption on the action sets and on two versions of the continuity assumption encapsulated as the continuous inclusion property (CIP). We show that the results are invariant to cardinality assumptions on the set of agents and on the dimension of the space in which the action sets are situated. This yields as special cases recent results in both mathematical economics and applied mathematics, and underscores the development of a rich and useful theory in bringing these two registers and two communities together.