Limiting distributions of the number of pure strategy Nash equilibria in N-person games
International Journal of Game Theory
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Formula Isomorphism Problem
SIAM Journal on Computing
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
Equilibria problems on games: Complexity versus succinctness
Journal of Computer and System Sciences
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We consider the question of when two games are equivalent and the computational complexity of deciding such a property for strategic games. We introduce three types of isomorphisms depending on which structure of the game is preserved: strict, weak, and local. We show that the computational complexity of the game isomorphism problem depends on the level of succinctness of the description of the input games but it is independent of the way the isomorphism is defined. Utilities or preferences in games can be represented by Turing machines (general form) or tables (explicit form). When the games are given in general form, we show that the game isomorphism problem is equivalent to the circuit isomorphism problem. When the games are given in explicit form, we show that the game isomorphism problem is equivalent to the graph isomorphism problem.