A pseudo-polynomial algorithm for mean payoff stochastic games with perfect information and a few random positions

  • Authors:

  • Endre Boros;Khaled Elbassioni;Vladimir Gurvich;Kazuhisa Makino

  • Affiliations:

  • RUTCOR, Rutgers University, Piscataway, NJ;Masdar Institute of Science and Technology, Abu Dhabi, UAE;RUTCOR, Rutgers University, Piscataway, NJ;Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto, Japan

  • Venue:
  • ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
  • Year:
  • 2013

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Abstract

We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G=(V, E), with local rewards r: E→ℝ, and three types of vertices: black VB, white VW, and random VR forming a partition of V. It is a long-standing open question whether a polynomial time algorithm for BWR-games exists, or not. In fact, a pseudo-polynomial algorithm for these games would already imply their polynomial solvability. In this paper, we show that BWR-games with a constant number of random nodes can be solved in pseudo-polynomial time. That is, for any such game with a few random nodes |VR|=O(1), a saddle point in pure stationary strategies can be found in time polynomial in |VW|+|VB|, the maximum absolute local reward R, and the common denominator of the transition probabilities.