Limiting distributions of the number of pure strategy Nash equilibria in N-person games
International Journal of Game Theory
On threshold circuits and polynomial computation
SIAM Journal on Computing
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
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 Formula Isomorphism Problem
SIAM Journal on Computing
The complexity of computations by networks
IBM Journal of Research and Development - Mathematics and computing
The computational complexity of nash equilibria in concisely represented games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Algorithmic Game Theory
Computer science and game theory
Communications of the ACM - Designing games with a purpose
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Monotone circuits for monotone weighted threshold functions
Information Processing Letters
Weighted Boolean formula games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Equilibria problems on games: Complexity versus succinctness
Journal of Computer and System Sciences
Computational Aspects of Uncertainty Profiles and Angel-Daemon Games
Theory of Computing Systems
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We address the question of whether two multiplayer strategic games are equivalent and the computational complexity of deciding such a property. We introduce two notions of isomorphisms, strong and weak. Each one of those isomorphisms preserves a different structure of the game. Strong isomorphisms are defined to preserve the utility functions and Nash equilibria. Weak isomorphisms preserve only the player's preference relations and thus pure Nash equilibria. 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 which of the two types of isomorphisms is considered. Utilities in games can be given succinctly by Turing machines, boolean circuits or boolean formulas, or explicitly by tables. Actions can be given both explicitly or succinctly. When the games are given in general form, we assume an explicit description of actions and a succinct description of utilities. We show that the game isomorphism problem for general form games is equivalent to the circuit isomorphism when utilities are described by TMs and to the boolean formula isomorphism problem when utilities are described by formulas. When the game is given in explicit form, we show that the game isomorphism problem is equivalent to the graph isomorphism problem.