On the complexity of game isomorphism

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: {it strict}, {it weak}, and {it local}. We show that the computa...

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Detalles Bibliográficos
Autores: Gabarró Vallès, Joaquim|||0000-0003-3771-2813, Garcia, Alina, Serna Iglesias, María José|||0000-0001-9729-8648
Tipo de recurso: informe técnico
Fecha de publicación:2007
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/86222
Acceso en línea:https://hdl.handle.net/2117/86222
Access Level:acceso abierto
Palabra clave:Game isomorphism
Succinct representations
Boolean formulas
Computational complexity
Boolean isomorphism
Graph isomorphism
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
Descripción
Sumario: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: {it strict}, {it weak}, and {it 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.