Structural complexity 2
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the NP-completeness of finding an optimal strategy in games with common payoffs
International Journal of Game Theory
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Pure Nash equilibria: hard and easy games
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
The computational complexity of equivalence and isomorphism problems
The computational complexity of equivalence and isomorphism problems
The NP-completeness column: Finding needles in haystacks
ACM Transactions on Algorithms (TALG)
On the Complexity of Equilibria Problems in Angel-Daemon Games
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Weighted Boolean formula games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Computing pure strategy nash equilibria in compact symmetric games
Proceedings of the 11th ACM conference on Electronic commerce
Equilibria problems on games: Complexity versus succinctness
Journal of Computer and System Sciences
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On the complexity of pure-strategy nash equilibria in congestion and local-effect games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Rational Generating Functions and Integer Programming Games
Operations Research
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
The Computational Complexity of Nash Equilibria in Concisely Represented Games
ACM Transactions on Computation Theory (TOCT)
On the complexity of game isomorphism
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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We study the computational complexity of deciding the existence of a Pure Nash Equilibrium in multi-player strategic games. We address two fundamental questions: how can we represent a game? and how can we represent a game with polynomial pay-off functions? Our results show that the computational complexity of deciding the existence of a pure Nash equilibrium in a strategic game depends on two parameters: the number of players and the size of the sets of strategies. In particular we show that deciding the existence of a Nash equilibrium in a strategic game is NP-complete when the number of players is large and the number of strategies for each player is constant, while the problem is Σ$^{p}_{\rm 2}$-complete when the number of players is a constant and the size of the sets of strategies is exponential (with respect to the length of the strategies).