Existence of equilibrium in an abstract economy without $SS$-convexity

TL;DR

This paper introduces $ ext{ extbackslash Delta}$-convexity in abstract economies with general topological choice sets, generalizing the classical equilibrium existence theorem by relaxing convexity assumptions.

Contribution

It extends the Yannelis-Prabhakar theorem to broader settings by replacing $SS$-convexity with $ ext{ extbackslash Delta}$-convexity, allowing for more general choice spaces.

Findings

Established the existence of equilibrium under $ ext{ extbackslash Delta}$-convexity

Generalized classical results to non-convex settings

Broadened applicability of equilibrium existence theorems

Abstract

In this paper, we introduce the concept of $\Delta$-convexity in an abstract economy with all choice sets being general topological spaces. We give a new generalization of the classical Yannelis-Prabhakar equilibrium existence theorem in abstract economies by relaxing $SS$-convexity to $\Delta$-convexity.