Equilibrium existence results for a class of discontinuous games

TL;DR

This paper introduces new mathematical concepts related to discontinuous games and proves fixed-point theorems, leading to novel equilibrium existence results for abstract economies and multiobjective games.

Contribution

It develops new notions of semicontinuity and fixed-point theorems, advancing the theoretical framework for analyzing equilibria in discontinuous game models.

Findings

New fixed-point theorem for w-lower semicontinuous correspondences

Existence of equilibrium in abstract economies with discontinuities

Application to generalized multiobjective games

Abstract

We introduce the notions of w-lower semicontinuous and almost w-lower semicontinuous correspondence with respect to a given set and prove a new fixed-point theorem. We also introduce the notion of correspondence with e-LSCS-property. As applications we obtain some new equilibrium theorems for abstract economies and for generalized multiobjective games.