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Beyond Admissibility: Dominance Between Chains of Strategies Basset, Nicolas Jecker, Ismaël Pauly, Arno Raskin, Jean-François Van den Bogaard, Marie dominated strategies admissible strategies games played on finite graphs reactive synthesis reachability games safety games cofinal order theory 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nicolas Basset and Ismaël Jecker and Arno Pauly and Jean-François Raskin and Marie Van den Bogaard 2018 Is Part Of LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2018.10 urn:nbn:de:0030-drops-96774 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.10 eng https://creativecommons.org/licenses/by/3.0/legalcode