Multi-player Equilibria Verification for Concurrent Stochastic Games

TL;DR

This paper introduces multi-coalitional verification methods for concurrent stochastic games, enabling the analysis of equilibria involving multiple distinct coalitions with complex objectives, extending existing two-coalition approaches.

Contribution

It extends verification techniques for CSGs to multiple coalitions, using subgame-perfect social welfare Nash equilibria and an enhanced logic for specifying properties.

Findings

Implemented in PRISM-games tool

Applied to secret sharing and public good case studies

Demonstrated effectiveness of multi-coalitional analysis

Abstract

Concurrent stochastic games (CSGs) are an ideal formalism for modelling probabilistic systems that feature multiple players or components with distinct objectives making concurrent, rational decisions. Examples include communication or security protocols and multi-robot navigation. Verification methods for CSGs exist but are limited to scenarios where agents or players are grouped into two coalitions, with those in the same coalition sharing an identical objective. In this paper, we propose multi-coalitional verification techniques for CSGs. We use subgame-perfect social welfare (or social cost) optimal Nash equilibria, which are strategies where there is no incentive for any coalition to unilaterally change its strategy in any game state, and where the total combined objectives are maximised (or minimised). We present an extension of the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) to specify equilibria-based properties for any number of distinct coalitions, and a corresponding model checking algorithm for a variant of stopping games. We implement our techniques in the PRISM-games tool and apply them to several case studies, including a secret sharing protocol and a public good game.