Geodesic
Strictly strong $(n-1)$-equilibrium in $n$-person multicriteria games
Contributions to game theory and management, Tome 7 (2014), pp. 181-190.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using some specific approach to the coalition-consistency analysis in $n$-person multicriteria games we introduce two refinements of (weak Pareto) equilibria: the strong and strictly strong $(n-1)$-equilibriums. Axiomatization of the strictly strong $(n-1)$-equilibria (on closed families of multicriteria games) is provided in terms of consistency, strong one-person rationality, suitable variants of Pareto optimality and converse consistency axiom and others.
Keywords: multicriteria games; Pareto equilibria; strong equilibrium; consistency; axiomatizations. 
@article{CGTM_2014_7_a15,
     author = {Denis V. Kuzyutin and Mariya V. Nikitina and Yaroslavna B. Pankratova},
     title = {Strictly strong $(n-1)$-equilibrium in $n$-person multicriteria games},
     journal = {Contributions to game theory and management},
     pages = {181--190},
     publisher = {mathdoc},
     volume = {7},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2014_7_a15/}
}
TY  - JOUR
AU  - Denis V. Kuzyutin
AU  - Mariya V. Nikitina
AU  - Yaroslavna B. Pankratova
TI  - Strictly strong $(n-1)$-equilibrium in $n$-person multicriteria games
JO  - Contributions to game theory and management
PY  - 2014
SP  - 181
EP  - 190
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2014_7_a15/
LA  - en
ID  - CGTM_2014_7_a15
ER  - 
%0 Journal Article
%A Denis V. Kuzyutin
%A Mariya V. Nikitina
%A Yaroslavna B. Pankratova
%T Strictly strong $(n-1)$-equilibrium in $n$-person multicriteria games
%J Contributions to game theory and management
%D 2014
%P 181-190
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2014_7_a15/
%G en
%F CGTM_2014_7_a15
Denis V. Kuzyutin; Mariya V. Nikitina; Yaroslavna B. Pankratova. Strictly strong $(n-1)$-equilibrium in $n$-person multicriteria games. Contributions to game theory and management, Tome 7 (2014), pp. 181-190. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a15/

[1] Aumann R. J., “Acceptable points in general cooperative $n$-person games”, Contributions to the theory of games, v. 4, Prinston, 1959, 287–324 | MR | Zbl

[2] Bernheim B., Peleg B., Winston M., “Coalition-proof Nash equilibria. I: Concept”, Journal of Economics Theory, 42 (1987), 1–12 | DOI | MR | Zbl

[3] Borm P., Van Megen F., Tijs S., “A perfectness concept for multicriteria games”, Mathematical Methods of Operation Research, 49 (1999), 401–412 | DOI | MR | Zbl

[4] Kaplan G., Sophisticated outcomes and coalitional stability, MSc Thesis, Department of Statistics, Tel-Aviv University, 1992

[5] Kuzyutin D., “On the problem of solutions' stability in extensive games”, Vestnik of St. Petersburg Univ., Ser. 1, 1995, no. 4, 18–23 (in Russian) | MR | Zbl

[6] Kuzyutin D., “Strong $(N-1)$-equilibrium. Concepts and axiomatic characterization”, International Journal of Mathematics, Game Theory and Algebra, 10:3 (2000), 217–226 | MR

[7] Kuzyutin D., “On the consistency of weak equilibria in multicriteria extensive games”, Collected papers, Contributions to game theory and management, 5, eds. L. A. Petrosjan, N. A. Zenkevich, St. Petersburg Univ. Press, 2012, 168–177

[8] Nash J. F., “Equilibrium points in $n$-person games”, Proc. Nat. Acad. Sci. USA, 36 (1950), 48–49 | DOI | MR | Zbl

[9] Norde H., Potters J., Reijnierse H., Vermeulen D., “Equilibrium selection and consistency”, Games and Economic Behavior, 12 (1996), 219–225 | DOI | MR | Zbl

[10] Peleg B., Potters J., Tijs S., “Minimality of consistent solutions for strategic games, in particular for potential games”, Economic Theory, 7 (1996), 81–93 | DOI | MR | Zbl

[11] Peleg B., Tijs S., “The consistency principle for games in strategic form”, International Journal of Game Theory, 25 (1996), 13–34 | DOI | MR | Zbl

[12] Petrosjan L., Kuzyutin D., Consistent solutions of positional games, St. Petersburg Univ. Press, 2008, 330 pp. (in Russian)

[13] Petrosjan L., Puerto J., “Folk theorems in multicriteria repeated $n$-person games”, Sociedad de Estatistica e Investigation Operativa Top, 10:2 (2002), 275–287 | MR | Zbl

[14] Shapley L., “Equilibrium points in games with vector payoffs”, Naval Research Logistics Quarterly, 1 (1959), 57–61 | DOI | MR

[15] Voorneveld M., Vermeulen D., Borm P., “Axiomatization of Pareto equilibria in multicriteria games”, Games and Economic Behavior, 28 (1999), 146–154 | DOI | MR | Zbl