On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games

TL;DR

This paper investigates the existence of subgame perfect and secure equilibria in multiplayer and two-player quantitative reachability games on graphs, introducing new concepts and algorithms for their determination.

Contribution

It introduces the concept of subgame perfect secure equilibrium and proves their existence in multiplayer games, also providing an algorithm to decide secure equilibrium existence.

Findings

Existence of subgame perfect equilibria in multiplayer games.

Existence of subgame perfect secure equilibria in two-player games.

An algorithm for deciding secure equilibria in multiplayer games.

Abstract

We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. secure equilibria) are guaranteed to exist in the multiplayer (resp. two-player) case. The existence of secure equilibria in the multiplayer case remained and is still an open problem. In this paper, we focus our study on the concept of subgame perfect equilibrium, a refinement of Nash equilibrium well-suited in the framework of games played on graphs. We also introduce the new concept of subgame perfect secure equilibrium. We prove the existence of subgame perfect equilibria (resp. subgame perfect secure equilibria) in multiplayer (resp. two-player) quantitative reachability games. Moreover, we provide an algorithm deciding the existence of secure equilibria in the multiplayer case.