# Nash equilibria in games over graphs equipped with a communication mechanism

## TL;DR

This paper investigates pure Nash equilibria in infinite-duration graph games with partial visibility and communication, proposing an epistemic approach to characterize equilibria through a simple reporting mechanism.

## Contribution

It introduces a novel epistemic game construction that captures players' knowledge and characterizes Nash equilibria using a simple communication pattern.

## Key findings

- Communication mechanism effectively characterizes Nash equilibria.
- Epistemic construction records players' knowledge for equilibrium analysis.
- Potential for efficient algorithms to compute equilibria based on the construction.

## Abstract

We study pure Nash equilibria in infinite-duration games on graphs, with partial visibility of actions but communication (based on a graph) among the players. We show that a simple communication mechanism consisting in reporting the deviator when seeing it and propagating this information is sufficient for characterizing Nash equilibria. We propose an epistemic game construction, which conveniently records important information about the knowledge of the players. With this abstraction, we are able to characterize Nash equilibria which follow the simple communication pattern via winning strategies. We finally discuss the size of the construction, which would allow efficient algorithmic solutions to compute Nash equilibria in the original game.