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The Operator Approach to Entropy Games Akian, Marianne Gaubert, Stéphane Grand-Clément, Julien Guillaud, Jérémie Stochastic games Shapley operators policy iteration Perron eigenvalues Risk sensitive control Entropy games and matrix multiplication games have been recently introduced by Asarin et al. They model the situation in which one player (Despot) wishes to minimize the growth rate of a matrix product, whereas the other player (Tribune) wishes to maximize it. We develop an operator approach to entropy games. This allows us to show that entropy games can be cast as stochastic mean payoff games in which some action spaces are simplices and payments are given by a relative entropy (Kullback-Leibler divergence). In this way, we show that entropy games with a fixed number of states belonging to Despot can be solved in polynomial time. This approach also allows us to solve these games by a policy iteration algorithm, which we compare with the spectral simplex algorithm developed by Protasov. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marianne Akian and Stéphane Gaubert and Julien Grand-Clément and Jérémie Guillaud 2017 Is Part Of LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2017.6 urn:nbn:de:0030-drops-70260 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.6 eng https://creativecommons.org/licenses/by/3.0/legalcode