Games on graphs with a public signal monitoring

TL;DR

This paper investigates Nash equilibria in graph-based games with imperfect public signal monitoring, introducing an epistemic abstraction to analyze players' knowledge and develop algorithms for specific payoff functions.

Contribution

It proposes a novel epistemic game abstraction to represent players' knowledge about deviations and characterizes Nash equilibria through winning strategies in this framework.

Findings

Epistemic abstraction effectively models players' knowledge about deviations.

Characterization of Nash equilibria via winning strategies.

Algorithms developed for certain payoff functions.

Abstract

We study pure Nash equilibria in games on graphs with an imperfect monitoring based on a public signal. In such games, deviations and players responsible for those deviations can be hard to detect and track. We propose a generic epistemic game abstraction, which conveniently allows to represent the knowledge of the players about these deviations, and give a characterization of Nash equilibria in terms of winning strategies in the abstraction. We then use the abstraction to develop algorithms for some payoff functions.