Infinitely Split Nash Equilibrium Problems in Repeated Games

TL;DR

This paper introduces the concept of infinitely split Nash equilibrium in repeated games with chain-complete posets, proving an existence theorem and applying it to a Bertrand duopoly model.

Contribution

It defines a new equilibrium concept in repeated games and establishes its existence using fixed point theorems, extending game theory analysis.

Findings

Existence of infinitely split Nash equilibrium proven.

Application to Bertrand duopoly model demonstrates practical relevance.

Provides a new framework for analyzing repeated games with complex strategy sets.

Abstract

In this paper, we introduce the concept of infinitely split Nash equilibrium in repeated games in which the profile sets are chain-complete posets. Then by using a fixed point theorem on posets in [8], we prove an existence theorem. As an application, we study the repeated extended Bertrant duopoly model of price competition.