Games through Nested Fixpoints

  • Thomas Martin Gawlitza
  • Helmut Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5643)


In this paper we consider two-player zero-sum payoff games on finite graphs, both in the deterministic as well as in the stochastic setting. In the deterministic setting, we consider total-payoff games which have been introduced as a refinement of mean-payoff games [10, 18]. In the stochastic setting, our class is a turn-based variant of liminf-payoff games [4, 15, 16]. In both settings, we provide a non-trivial characterization of the values through nested fixpoint equations. The characterization of the values of liminf-payoff games moreover shows that solving liminf-payoff games is polynomial-time reducible to solving stochastic parity games. We construct practical algorithms for solving the occurring nested fixpoint equations based on strategy iteration. As a corollary we obtain that solving deterministic total-payoff games and solving stochastic liminf-payoff games is in UP ∩ co− UP.


Strategy Improvement Stochastic Game Hierarchical System Variable Assignment Optimality Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Thomas Martin Gawlitza
    • 1
  • Helmut Seidl
    • 1
  1. 1.TU München, Institut für Informatik, I2MünchenGermany

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