dc.contributor.author Boros, Endre dc.contributor.author Elbassioni, Khaled dc.contributor.author Fouz, Mahmoud dc.contributor.author Gurvich, Vladimir dc.contributor.author Manthey, Bodo dc.date.accessioned 2010-03-20T12:01:00Z dc.date.accessioned 2016-10-05T14:14:17Z dc.date.available 2010-03-20T12:01:00Z dc.date.available 2016-10-05T14:14:17Z dc.date.issued 2010-03-20 dc.identifier.uri http://publications.mfo.de/handle/mfo/1176 dc.description Research in Pairs 2010 en_US dc.description.abstract We consider two-person zero-sum stochastic mean payoff games with perfect information modeled by a digraph with black, white, and random vertices. These BWR-games games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games, stochastic parity games, and Markov decision processes. They can also be used to model parlor games such as Chess or Backgammon. It is a long-standing open question whether a polynomial algorithm exists that solves BWR-games. In fact, a pseudo-polynomial algorithm for these games with an arbitrary number of random nodes would already imply their polynomial solvability. Currently, only two classes are known to have such a pseudo-polynomial algorithm: BW-games (the case with no random nodes) and ergodic BWR-games (i.e., in which the game's value does not depend on the initial position) with constant number of random nodes. In this paper, we show that the existence of a pseudo-polynomial algorithm for BWR-games with constant number of random vertices implies smoothed polynomial time complexity and the existence of absolute and relative polynomial-time approximation schemes. In particular, we obtain smoothed polynomial time complexity and derive absolute and relative approximation schemes for the above two classes. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2010,22 dc.title Stochastic mean payoff game: smoothed analysis and approximation schemes en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2010-22 local.scientificprogram Research in Pairs 2010 local.series.id OWP-2010-22
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