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DOI: 10.4230/LIPIcs.CSL.2024.32

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

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

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract

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.

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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)

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@InProceedings{gutierrez_et_al:LIPIcs.CSL.2024.32,
  author =	{Gutierrez, Julian and Lin, Anthony W. and Najib, Muhammad and Steeples, Thomas and Wooldridge, Michael},
  title =	{{Characterising and Verifying the Core in Concurrent Multi-Player Mean-Payoff Games}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{32:1--32:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.32},
  URN =		{urn:nbn:de:0030-drops-196752},
  doi =		{10.4230/LIPIcs.CSL.2024.32},
  annote =	{Keywords: Concurrent games, multi-agent systems, temporal logic, game theory}
}

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

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