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
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Correlated equilibria in graphical games
Proceedings of the 4th ACM conference on Electronic commerce
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Computing correlated equilibria in multi-player games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the Complexity of Succinct Zero-Sum Games
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Graphical models for game theory
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Reducibility among equilibrium problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The computational complexity of nash equilibria in concisely represented games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Computing correlated equilibria in multi-player games
Journal of the ACM (JACM)
Nash Stability in Additively Separable Hedonic Games Is NP-Hard
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Equilibria of Graphical Games with Symmetries
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Pure Nash equilibria: complete characterization of hard and easy graphical games
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Equilibria of graphical games with symmetries
Theoretical Computer Science
Equilibria problems on games: Complexity versus succinctness
Journal of Computer and System Sciences
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)
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We present algorithms and complexity results for the problem of finding equilibria (mixed Nash equilibria, pure Nash equilibria and correlated equilibria) in games with extremely succinct description that are defined on highly regular graphs such as the d-dimensional grid; we argue that such games are of interest in the modelling of large systems of interacting agents. We show that mixed Nash equilibria can be found in time exponential in the succinct representation by quantifier elimination, while correlated equilibria can be found in polynomial time by taking advantage of the game’s symmetries. Finally, the complexity of determining whether such a game on the d-dimensional grid has a pure Nash equilibrium depends on d and the dichotomy is remarkably sharp: it is solvable in polynomial time (in fact NL-complete) when d = 1, but it is NEXP-complete for d ≥ 2.