Characterising and Verifying the Core in Concurrent Multi-Player Mean-Payoff Games

Authors Julian Gutierrez, Anthony W. Lin , Muhammad Najib , Thomas Steeples, Michael Wooldridge

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Author Details

Julian Gutierrez
  • Monash University, Clayton, Australia
Anthony W. Lin
  • University of Kaiserslautern-Landau, Germany
  • Max-Planck Institute for Software Systems, Kaiserslautern, Germany
Muhammad Najib
  • Heriot-Watt University, Edinburgh, UK
Thomas Steeples
  • University of Oxford, UK
Michael Wooldridge
  • University of Oxford, UK


We wish to thank anonymous reviewers for their useful feedback.

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Julian Gutierrez, Anthony W. Lin, Muhammad Najib, Thomas Steeples, and Michael Wooldridge. Characterising and Verifying the Core in Concurrent Multi-Player Mean-Payoff Games. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 32:1-32:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Concurrent multi-player mean-payoff games are important models for systems of agents with individual, non-dichotomous preferences. Whilst these games have been extensively studied in terms of their equilibria in non-cooperative settings, this paper explores an alternative solution concept: the core from cooperative game theory. This concept is particularly relevant for cooperative AI systems, as it enables the modelling of cooperation among agents, even when their goals are not fully aligned. Our contribution is twofold. First, we provide a characterisation of the core using discrete geometry techniques and establish a necessary and sufficient condition for its non-emptiness. We then use the characterisation to prove the existence of polynomial witnesses in the core. Second, we use the existence of such witnesses to solve key decision problems in rational verification and provide tight complexity bounds for the problem of checking whether some/every equilibrium in a game satisfies a given LTL or GR(1) specification. Our approach is general and can be adapted to handle other specifications expressed in various fragments of LTL without incurring additional computational costs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Verification by model checking
  • Theory of computation → Solution concepts in game theory
  • Concurrent games
  • multi-agent systems
  • temporal logic
  • game theory


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