Games through nested fixpoints

Thomas Martin Gawlitza, Helmut Seidl

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

14 Scopus citations


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.

Original languageEnglish
Title of host publicationComputer Aided Verification - 21st International Conference, CAV 2009, Proceedings
Number of pages15
StatePublished - 2009
Event21st International Conference on Computer Aided Verification, CAV 2009 - Grenoble, France
Duration: 26 Jun 20092 Jul 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5643 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference21st International Conference on Computer Aided Verification, CAV 2009


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