LIPIcs.CSL.2025.23.pdf
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Permissive Equilibria in Multiplayer Reachability Games
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Benjamin Monmege 
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33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Computer Science Logic (CSL) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2025-02-03
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Aline Goeminne and Benjamin Monmege. Permissive Equilibria in Multiplayer Reachability Games. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
https://doi.org/10.4230/LIPIcs.CSL.2025.23
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 [Patricia Bouyer et al., 2009]. We show that we can decide the existence of a multi-strategy profile 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.
Subject Classification
ACM Subject Classification
- Software and its engineering → Formal methods
- Theory of computation → Logic and verification
- Theory of computation → Solution concepts in game theory
Keywords
- multiplayer reachability games
- penalties
- permissive equilibria
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References
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