On Equilibria in Quantitative Games with Reachability/Safety Objectives

TL;DR

This paper investigates the existence of finite-memory Nash and secure equilibria in multiplayer and two-player quantitative games on finite graphs with reachability and safety objectives.

Contribution

It proves the existence of finite-memory Nash equilibria in multiplayer games and secure equilibria in two-player reachability games with these objectives.

Findings

Finite-memory Nash equilibria exist in multiplayer reachability/safety games.

Finite-memory secure equilibria exist in two-player reachability games.

Results apply to games played on finite graphs with specific objectives.

Abstract

In this paper, we study turn-based quantitative multiplayer non zero-sum games played on finite graphs with both reachability and safety objectives. In this framework a player with a reachability objective aims at reaching his own goal as soon as possible, whereas a player with a safety objective aims at avoiding his bad set or, if impossible, delaying its visit as long as possible. We prove the existence of Nash equilibria with finite memory in quantitative multiplayer reachability/safety games. Moreover, we prove the existence of finite-memory secure equilibria for quantitative two-player reachability games.