Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
Alternating-time temporal logic
Journal of the ACM (JACM)
Complexity of weak acceptance conditions in tree automata
Information Processing Letters
Infinite Games and Verification (Extended Abstract of a Tutorial)
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Games in system design and verification
TARK '05 Proceedings of the 10th conference on Theoretical aspects of rationality and knowledge
The complexity of Nash equilibria in infinite multiplayer games
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Nash equilibria for reachability objectives in multi-player timed games
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
The complexity of nash equilibria in limit-average games
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Complexity bounds for regular games
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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 consider concurrent games played on graphs, in which each player has several qualitative (e.g. reachability or Büchi) objectives, and a preorder on these objectives (for instance the counting order, where the aim is to maximise the number of objectives that are fulfilled). We study two fundamental problems in that setting: (1) the value problem, which aims at deciding the existence of a strategy that ensures a given payoff; (2) the Nash equilibrium problem, where we want to decide the existence of a Nash equilibrium (possibly with a condition on the payoffs). We characterise the exact complexities of these problems for several relevant preorders, and several kinds of objectives.