# Stochastic mean payoff games: smoothed analysis and approximation schemes

Boros, Endre
and
Elbassioni, Khaled
and
Fouz, Mahmoud
and
Gurvich, Vladimir
and
Makino, Kazuhisa
and
Manthey, Bodo
(2011)
*Stochastic mean payoff games: smoothed analysis and approximation schemes.*
In: 38th International Colloquium on Automata, Languages and Programming, ICALP 2011, 4-8 July 2011, Zurich, Switzerland (pp. pp. 147-158).

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Abstract: | In this paper, we consider two-player 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 if 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 (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 complexity and the existence of absolute and relative polynomial-time approximation schemes. In particular, we obtain smoothed polynomial complexity and derive absolute and relative approximation schemes for BW-games and ergodic BWR-games (assuming a technical requirement about the probabilities at the random nodes). |

Item Type: | Conference or Workshop Item |

Copyright: | © 2011 Springer |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/78128 |

Official URL: | http://dx.doi.org/10.1007/978-3-642-22006-7_13 |

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