Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Computing pure nash equilibria in graphical games via markov random fields
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
The computational complexity of nash equilibria in concisely represented games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
The influence of neighbourhood and choice on the complexity of finding pure Nash equilibria
Information Processing Letters
Computing correlated equilibria in multi-player games
Journal of the ACM (JACM)
On the Complexity of Equilibria Problems in Angel-Daemon Games
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Symmetries and the complexity of pure Nash equilibrium
Journal of Computer and System Sciences
Pure Nash equilibria: hard and easy games
Journal of Artificial Intelligence Research
Complexity of pure equilibria in Bayesian games
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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
Weighted Boolean formula games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
The complexity of games on highly regular graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Atomic selfish routing in networks: a survey
WINE'05 Proceedings of the First international conference on Internet and Network Economics
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
The game world is flat: the complexity of nash equilibria in succinct games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Pure nash equilibria in games with a large number of actions
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
On the complexity of game isomorphism
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
The complexity of game isomorphism
Theoretical Computer Science
Computational Aspects of Uncertainty Profiles and Angel-Daemon Games
Theory of Computing Systems
Hi-index | 0.00 |
We study the computational complexity of problems involving equilibria in strategic games and in perfect information extensive games when the number of players is large. We consider, among others, the problems of deciding the existence of a pure Nash equilibrium in strategic games or deciding the existence of a pure Nash or a subgame perfect Nash equilibrium with a given payoff in finite perfect information extensive games. We address the fundamental question of how can we represent a game with a large number of players? We propose three ways of representing a game with different degrees of succinctness for the components of the game. For perfect information extensive games we show that when the number of moves of each player is large and the input game is represented succinctly these problems are PSPACE-complete. In contraposition, when the game is described explicitly by means of its associated tree all these problems are decidable in polynomial time. For strategic games we show that the complexity of deciding the existence of a pure Nash equilibrium depends on the succinctness of the game representation and then on the size of the action sets. In particular we show that it is NP-complete, when the number of players is large and the number of actions for each player is constant, and that the problem is @S"2^p-complete when the number of players is a constant and the size of the action sets is exponential in the size of the game representation. Again when the game is described explicitly the problem is decidable in polynomial time.