Stochastic Equilibria under Imprecise Deviations in Terminal-Reward Concurrent Games

TL;DR

This paper introduces a relaxed equilibrium concept in concurrent graph games with terminal rewards, proving existence and providing a PSPACE algorithm for computation, addressing limitations of traditional Nash equilibria.

Contribution

The paper presents a new notion of equilibria with imprecise deviations, ensuring existence where Nash equilibria may not, and offers an algorithm for their computation.

Findings

Imprecise deviation equilibria always exist in the studied setting.

A PSPACE algorithm can compute these equilibria.

Traditional Nash equilibria may not exist under certain objectives.

Abstract

We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward objectives, and their existence is undecidable with qualitative reachability objectives (and only three players). However, these results rely on the fact that the players can enforce infinite plays while trying to improve their payoffs. In this paper, we introduce a relaxed notion of equilibria, where deviations are imprecise. We prove that contrary to Nash equilibria, such (stationary) equilibria always exist, and we develop a PSPACE algorithm to compute one.