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Games through Nested Fixpoints (2009)
| Citations: | 5 - 0 self |
BibTeX
@MISC{Gawlitza09gamesthrough,
author = {Thomas Martin Gawlitza and Helmut Seidl},
title = {Games through Nested Fixpoints},
year = {2009}
}
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Abstract
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 [18, 10]. In the stochastic setting, our class is a turn-based variant of liminf-payoff games [15, 16, 4]. 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.
Keyphrases
liminf-payoff game fixpoint equation stochastic setting two-player zero-sum payoff game stochastic parity game finite graph strategy iteration total-payoff game non-trivial characterization mean-payoff game practical algorithm deterministic setting turn-based variant deterministic total-payoff game stochastic liminf-payoff game
