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On the hardness of game equivalence under localisomorphism∗

Published online by Cambridge University Press:  05 November 2012

Joaquim Gabarró ,
Alina García  and
Maria Serna
Joaquim Gabarró
Affiliation:
ALBCOM Research Group, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Ω Building, 08034 Barcelona, Spain. . gabarro@lsi.upc.edu, agarcia@lsi.upc.edu, mjserna@lsi.upc.edu
Alina García
Affiliation:
ALBCOM Research Group, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Ω Building, 08034 Barcelona, Spain. . gabarro@lsi.upc.edu, agarcia@lsi.upc.edu, mjserna@lsi.upc.edu
Maria Serna
Affiliation:
ALBCOM Research Group, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Ω Building, 08034 Barcelona, Spain. . gabarro@lsi.upc.edu, agarcia@lsi.upc.edu, mjserna@lsi.upc.edu
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Abstract

We introduce a type of isomorphism among strategic games that we call localisomorphism. Local isomorphisms is a weaker version of the notions of strongand weak game isomorphism introduced in [J. Gabarro, A. Garcia and M. Serna,Theor. Comput. Sci. 412 (2011) 6675–6695]. In a localisomorphism it is required to preserve, for any player, the player’s preferences on thesets of strategy profiles that differ only in the action selected by this player. We showthat the game isomorphism problem for local isomorphism is equivalent to the same problemfor strong or weak isomorphism for strategic games given in: general, extensive andformula general form. As a consequence of the results in [J. Gabarro, A. Garcia and M.Serna, Theor. Comput. Sci. 412 (2011) 6675–6695] thisimplies that local isomorphism problem for strategic games is equivalent to (a) thecircuit isomorphism problem for games given in general form, (b) the boolean formulaisomorphism problem for formula games in general form, and (c) the graph isomorphismproblem for games given in explicit form.

Keywords

Game isomorphismsuccinct representationsstrategic gamesformula gamescomputational complexitycircuit isomorphismboolean formula isomorphismgraph isomorphism
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 47 , Issue 2 , April 2013 , pp. 147 - 169
Copyright
© EDP Sciences 2012

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