# On the hardness of game equivalence under local isomorphism

Joaquim Gabarró; Alina García; Maria Serna

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2013)

- Volume: 47, Issue: 2, page 147-169
- ISSN: 0988-3754

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topGabarró, Joaquim, García, Alina, and Serna, Maria. "On the hardness of game equivalence under local isomorphism." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 47.2 (2013): 147-169. <http://eudml.org/doc/273051>.

@article{Gabarró2013,

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

author = {Gabarró, Joaquim, García, Alina, Serna, Maria},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {game isomorphism; succinct representations; strategic games; formula games; computational complexity; circuit isomorphism; boolean formula isomorphism; graph isomorphism; Boolean formula isomorphism},

language = {eng},

number = {2},

pages = {147-169},

publisher = {EDP-Sciences},

title = {On the hardness of game equivalence under local isomorphism},

url = {http://eudml.org/doc/273051},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Gabarró, Joaquim

AU - García, Alina

AU - Serna, Maria

TI - On the hardness of game equivalence under local isomorphism

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 2

SP - 147

EP - 169

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

LA - eng

KW - game isomorphism; succinct representations; strategic games; formula games; computational complexity; circuit isomorphism; boolean formula isomorphism; graph isomorphism; Boolean formula isomorphism

UR - http://eudml.org/doc/273051

ER -

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