Permissive Equilibria in Multiplayer Reachability Games

TL;DR

This paper investigates multi-strategies in multiplayer reachability games on finite graphs, focusing on their permissiveness, equilibrium properties, and computational decidability under penalty constraints.

Contribution

It introduces methods to decide the existence of permissive multi-strategies forming Nash or subgame perfect equilibria within PSPACE, considering penalty bounds and winning conditions.

Findings

Decidability of multi-strategy existence in PSPACE with unary penalties

Extension of two-player zero-sum penalty concepts to multiplayer settings

Algorithms for verifying equilibrium conditions under penalty constraints

Abstract

We study multi-strategies in multiplayer reachability games played on finite graphs. A multi-strategy prescribes a set of possible actions, instead of a single action as usual strategies: it represents a set of all strategies that are consistent with it. We aim for profiles of multi-strategies (a multi-strategy per player), where each profile of consistent strategies is a Nash equilibrium, or a subgame perfect equilibrium. The permissiveness of two multi-strategies can be compared with penalties, as already used in the two-player zero-sum setting by Bouyer, Duflot, Markey and Renault. We show that we can decide the existence of a multi-strategy that is a Nash equilibrium or a subgame perfect equilibrium, while satisfying some upper-bound constraints on the penalties in PSPACE, if the upper-bound penalties are given in unary. The same holds when we search for multi-strategies where certain players are asked to win in at least one play or in all plays