# Two-player nonzero-sum ω-regular games

Chatterjee K. 2005. Two-player nonzero-sum ω-regular games. CONCUR: Concurrency Theory, LNCS , vol. 3653, 413–427.

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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.

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Date Published

2005-09-05

Volume

3653

Page

413 - 427

Conference

CONCUR: Concurrency Theory

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### Cite this

Chatterjee K. Two-player nonzero-sum ω-regular games. In: Vol 3653. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2005:413-427. doi:10.1007/11539452_32

Chatterjee, K. (2005). Two-player nonzero-sum ω-regular games (Vol. 3653, pp. 413–427). Presented at the CONCUR: Concurrency Theory, Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.1007/11539452_32

Chatterjee, Krishnendu. “Two-Player Nonzero-Sum ω-Regular Games,” 3653:413–27. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2005. https://doi.org/10.1007/11539452_32.

K. Chatterjee, “Two-player nonzero-sum ω-regular games,” presented at the CONCUR: Concurrency Theory, 2005, vol. 3653, pp. 413–427.

Chatterjee, Krishnendu.

*Two-Player Nonzero-Sum ω-Regular Games*. Vol. 3653, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2005, pp. 413–27, doi:10.1007/11539452_32.