Split Nash Equilibria for Related Games and Applications to Economics

TL;DR

This paper introduces split Nash equilibrium problems for related strategic games, proves their existence using Fan-KKM theorem, and applies the results to economic models like duopoly and related economies.

Contribution

It defines split Nash equilibrium for related games and establishes their existence in Banach spaces, extending equilibrium analysis in economics.

Findings

Existence of split Nash equilibria in related noncooperative games

Application of Fan-KKM theorem to prove equilibrium existence

Demonstration in economic models like duopoly and interconnected economies

Abstract

In this paper we introduce the concept of split Nash equilibrium problems associated with two related noncooperative strategic games. Then we apply the Fan-KKM theorem to prove the existence of solutions to split Nash equilibrium problems of related noncooperative strategic games, in which the strategy sets of the players are nonempty closed and convex subsets in Banach spaces. As application of this existence to economics, an example is provided to study the existence of split Nash equilibrium of utilities of two related economies. As applications, we study the existence of split Nash equilibrium in the dual extended Bertrant duopoly model of price competition