A simple algorithm for computing Nash-equilibria in incomplete information games

Abstract : We present a simple projection-free primal-dual algorithm for computing approximate Nash-equilibria in two-person zero-sum sequential games with incomplete information and perfect recall (like Texas Hold’em Poker). Our algorithm is numerically stable, performs only basic iterations (i.e matvec multiplications, clipping, etc., and no calls to external first-order oracles, no matrix inversions, etc.), and is applicable to a broad class of two-person zero-sum games including simultaneous games and sequential games with incomplete information and perfect recall. The applicability to the latter kind of games is thanks to the sequence-form representation which allows one to encode such a game as a matrix game with convex polytopial strategy profiles. We prove that the number of iterations needed to produce a Nash-equilibrium with a given precision is inversely proportional to the precision. We present experimental results on matrix games on simplexes and Kuhn Poker.
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Communication dans un congrès
OPT2016 -- NIPS workshop on optimization for machine learning, Dec 2016, Barcelona, Spain. 2016, 〈http://opt-ml.org/〉
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Dernière modification le : samedi 18 février 2017 - 01:14:34

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Elvis Dohmatob. A simple algorithm for computing Nash-equilibria in incomplete information games. OPT2016 -- NIPS workshop on optimization for machine learning, Dec 2016, Barcelona, Spain. 2016, 〈http://opt-ml.org/〉. 〈hal-01384460〉

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