Geodesic
Homomorphisms and Congruence Relations for Games with Preference Relations
Contributions to game theory and management, Tome 3 (2010), pp. 387-398.

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In this paper we consider games with preference relations. The main optimality concept for such games is concept of equilibrium. We introduce a notion of homomorphism for games with preference relations and study a problem concerning connections between equilibrium points of games which are in a homomorphic relation. The main result is finding covariantly and contravariantly complete families of homomorphisms.
Keywords: homomorphism, equilibrium points, Nash equilibrium, game with preference relations. 
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     author = {Tatiana F. Savina},
     title = {Homomorphisms and {Congruence} {Relations} for {Games} with {Preference} {Relations}},
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     url = {http://geodesic.mathdoc.fr/item/CGTM_2010_3_a28/}
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Tatiana F. Savina. Homomorphisms and Congruence Relations for Games with Preference Relations. Contributions to game theory and management, Tome 3 (2010), pp. 387-398. http://geodesic.mathdoc.fr/item/CGTM_2010_3_a28/

[1] Birkhoff G., Lattice theory, Amer. Math. Soc. Coll. Publ., 25, 1967 | Zbl

[2] Savina T. F., “Mathematical Models for Games, Based on Preference Relations”, Game Theory and Management, Collected abstracts of papers presented on the Third International Conference Game Theory and Management, Graduate School of Management SPbU, SPb., 2009, 227–228

[3] Savina T. F., “Covariant and Contrvariant Homomorphisms of Games with Preference Relations”, Izvestya SGU, 9:3 (2009), 66–70 (in Russian)