Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
Modalities for model checking (extended abstract): branching time strikes back
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
DAG-width: connectivity measure for directed graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Rational behaviour and strategy construction in infinite multiplayer games
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Decision problems for Nash equilibria in stochastic games
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Computing equilibria in two-player timed games via turn-based finite games
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
Nash equilibria for reachability objectives in multi-player timed games
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
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
Nash equilibrium in weighted concurrent timed games with reachability objectives
ICDCIT'12 Proceedings of the 8th international conference on Distributed Computing and Internet Technology
Concurrent games with ordered objectives
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
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 the complexity of Nash equilibria in infinite (turnbased, qualitative) multiplayer games. Chatterjee & al. showed the existence of a Nash equilibrium in any such game with ω-regular winning conditions, and they devised an algorithm for computing one. We argue that in applications it is often insufficient to compute just some Nash equilibrium. Instead, we enrich the problem by allowing to put (qualitative) constraints on the payoff of the desired equilibrium. Our main result is that the resulting decision problem is NP-complete for games with co-Büchi, parity or Streett winning conditions but fixed-parameter tractable for many natural restricted classes of games with parity winning conditions. For games with Büchi winning conditions we show that the problem is, in fact, decidable in polynomial time. We also analyse the complexity of strategies realising a Nash equilibrium. In particular, we show that pure finite-state strategies as opposed to arbitrary mixed strategies suffice to realise any Nash equilibrium of a game with ω-regular winning conditions with a qualitative constraint on the payoff.