Two-player nonZero-sum stopping games in discrete time

TL;DR

This paper proves that in discrete-time two-player nonzero-sum stopping games, approximate equilibria exist using a novel stochastic Ramsey's theorem approach, simplifying the analysis to finite state spaces.

Contribution

Introduces a stochastic Ramsey's theorem-based method to establish the existence of psilon-equilibria in complex nonzero-sum stopping games.

Findings

Existence of psilon-equilibria in all such games

Reduction of complex games to finite state space analysis

Application of stochastic Ramsey's theorem in game theory

Abstract

We prove that every two-player nonzero-sum stopping game in discrete time admits an \epsilon-equilibrium in randomized strategies for every \epsilon >0. We use a stochastic variation of Ramsey's theorem, which enables us to reduce the problem to that of studying properties of \epsilon-equilibria in a simple class of stochastic games with finite state space.