Two-player nonzero-sum ω-regular games Conference Paper

Author(s): Chatterjee, Krishnendu
Title: Two-player nonzero-sum ω-regular games
Title Series: LNCS
Abstract: We study infinite stochastic games played by two-players on a finite graph with goals specified by sets of infinite traces. The games are concurrent (each player simultaneously and independently chooses an action at each round), stochastic (the next state is determined by a probability distribution depending on the current state and the chosen actions), infinite (the game continues for an infinite number of rounds), nonzero-sum (the players' goals are not necessarily conflicting), and undiscounted. We show that if each player has an W-regular objective expressed as a paxity objective, then there exists an epsilon-Nash equilibrium, for every epsilon > 0. However, exact Nash equilibria need not exist. We study the complexity of finding values (payoff profile) of an epsilon-Nash equilibrium. We show that the values of an epsilon-Nash equilibrium in nonzero-sum concurrent parity games can be computed by solving the following two simpler problems: computing the values of zero-sum (the goals of the players axe strictly conflicting) concurrent parity games and computing epsilon-Nash equilibrium values of nonzero-sum concurrent games with reachability objectives. As a consequence we establish that values of an epsilon-Nash equilibrium can be computed in TFNP (total functional NP), and hence in EXPTIME.
Conference Title: CONCUR: Concurrency Theory
Volume: 3653
Conference Dates: August 23-26, 2005
Conference Location: San Francisco, CA, USA
ISBN: 978-3-95977-017-0
Publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik  
Date Published: 2005-09-05
Start Page: 413
End Page: 427
DOI: 10.1007/11539452_32
Open access: no
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