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...
| Autores: | , , |
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| 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 |
| 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. |
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