On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Languages, automata, and logic
Handbook of formal languages, vol. 3
Quantitative solution of omega-regular games380872
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Concurrent Omega-Regular Games
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QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Automatic verification of probabilistic concurrent finite state programs
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A survey of stochastic ω-regular games
Journal of Computer and System Sciences
Nash equilibrium for upward-closed objectives
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PRALINE: a tool for computing nash equilibria in concurrent games
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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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 ω-regular objective expressed as a parity objective, then there exists an MediaObjects/InlineFigure1.png-Nash equilibrium, for every MediaObjects/InlineFigure2.png. However, exact Nash equilibria need not exist. We study the complexity of finding values (payoff profile) of an MediaObjects/InlineFigure3.png-Nash equilibrium. We show that the values of an MediaObjects/InlineFigure4.png-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 are strictly conflicting) concurrent parity games and computing MediaObjects/InlineFigure5.png-Nash equilibrium values of nonzero-sum concurrent games with reachability objectives. As a consequence we establish that values of an MediaObjects/InlineFigure6.png-Nash equilibrium can be computed in TFNP (total functional NP), and hence in EXPTIME.