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Admissiblity in Concurrent Games

Authors Nicolas Basset, Gilles Geeraerts, Jean-François Raskin, Ocan Sankur

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Nicolas Basset
Gilles Geeraerts
Jean-François Raskin
Ocan Sankur

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Nicolas Basset, Gilles Geeraerts, Jean-François Raskin, and Ocan Sankur. Admissiblity in Concurrent Games. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 123:1-123:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ICALP.2017.123

Abstract

In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays 'as well as possible', because there is no other strategy that dominates it, i.e., that wins (almost surely) against a superset of adversarial strategies. We prove that admissible strategies always exist in concurrent games, and we characterise them precisely. Then, when the objectives of the players are omega-regular, we show how to perform assume-admissible synthesis, i.e., how to compute admissible strategies that win (almost surely) under the hypothesis that the other players play admissible strategies only.
Keywords
  • Multi-player games
  • admissibility
  • concurrent games
  • randomized strategies

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