Fair Adversaries and Randomization in Two-Player Games

  • Eugene Asarin
  • Raphaël Chane-Yack-Fa
  • Daniele Varacca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6014)


Two-player games are used to model open systems. One player models the system, trying to respect some specification, while the other player models the environment. In classical model checking, the objective is to verify that the system can respect its specification, whatever the environment does.

In this article, we consider a more realistic scenario when the environment is supposed to be fair. We define a notion of fair player in two-player games. Our solution is inspired by Banach-Mazur games, and leads to a definition of a novel class of 3-player games called ABM-games. For ω-regular specifications on finite arenas, we explore the properties of ABM-games and devise an algorithm for solving them. As the main result, we show that winning in an ABM-game (i.e. winning against a fair player) is equivalent to winning with probability one against the randomized adversary.


Games Markov decision processes fairness 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Eugene Asarin
    • 1
  • Raphaël Chane-Yack-Fa
    • 2
  • Daniele Varacca
    • 3
  1. 1.LIAFACNRS & Univ. Paris DiderotFrance
  2. 2.Département d’informatiqueUniv. de SherbrookeCanada
  3. 3.PPSCNRS & Univ. Paris DiderotFrance

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