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Beyond Admissibility: Dominance Between Chains of Strategies

Authors Nicolas Basset, Ismaël Jecker, Arno Pauly , Jean-François Raskin, Marie Van den Bogaard

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Author Details

Nicolas Basset
  • Université Grenoble Alpes, Grenoble, France
Ismaël Jecker
  • Department of Computer Science, Université Libre de Bruxelles, Brussels, Belgium
Arno Pauly
  • Department of Computer Science, Swansea University, Swansea, UK
Jean-François Raskin
  • Department of Computer Science, Université Libre de Bruxelles, Brussels, Belgium
Marie Van den Bogaard
  • Department of Computer Science, Université Libre de Bruxelles, Brussels, Belgium

Funding

This work was partially supported by the ERC inVEST (279499), the ARC project "Non-Zero Sum Game Graphs: Applications to Reactive Synthesis and Beyond" (Fédération Wallonie-Bruxelles), the EOS project "Verifying Learning Artificial Intelligence Systems" (FNRS-FWO), and the Belgian FNRS PDR project "Subgame perfection in graph games" (T.0088.18). J.-F. Raskin is Professeur Francqui de Recherche funded by the Francqui foundation.

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Nicolas Basset, Ismaël Jecker, Arno Pauly, Jean-François Raskin, and Marie Van den Bogaard. Beyond Admissibility: Dominance Between Chains of Strategies. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CSL.2018.10

Abstract

Admissible strategies, i.e. those that are not dominated by any other strategy, are a typical rationality notion in game theory. In many classes of games this is justified by results showing that any strategy is admissible or dominated by an admissible strategy. However, in games played on finite graphs with quantitative objectives (as used for reactive synthesis), this is not the case.
We consider increasing chains of strategies instead to recover a satisfactory rationality notion based on dominance in such games. We start with some order-theoretic considerations establishing sufficient criteria for this to work. We then turn our attention to generalised safety/reachability games as a particular application. We propose the notion of maximal uniform chain as the desired dominance-based rationality concept in these games. Decidability of some fundamental questions about uniform chains is established.

Subject Classification

ACM Subject Classification
  • Theory of computation → Solution concepts in game theory
  • Theory of computation → Automata extensions
Keywords
  • dominated strategies
  • admissible strategies
  • games played on finite graphs
  • reactive synthesis
  • reachability games
  • safety games
  • cofinal
  • order theory

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