Solutions for network games and symmetric group representations

• Autorzy: Sánchez-Pérez Joss

Identyfikatory

DOI

10.37190/ord190405

• Języki publikacji: EN

Abstrakty

EN

We present the relationship between network games and representation theory of the group of permutations of the set of players (nodes), and also offer a different perspective to study solutions for this kind of problems. We then provide several applications of this approach to the cases with three and four players.

Słowa kluczowe

EN

network game; axiomatic solutions; representation theory; symmetric group

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2019
• Tom: Vol. 29, No. 4
• Strony: 95--123
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Sánchez-Pérez Joss

• Facultad de Economía, UASLP, Av. Pintores s/n, Burócratas del Estado, C.P. 78213, San Luis Potosí, SLP, México

Bibliografia

• [1] AUMANN R., MYERSON R., Endogenous formation of links between players and coalitions: an application of the Shapley value, [In:] A. Roth (Ed.), The Shapley Value, Cambridge University Press, 1988, 175–191.
• [2] CRISMAN K., ORRISON M., Representation theory of the symmetric group in voting theory and game theory, Cont. Math., 2017, 685, 97–116.
• [3] FULTON W., HARRIS J., Representation Theory. A first course, Springer-Verlag Graduate Texts in Mathematics, New York 1991, 129.
• [4] HERNÁNDEZ-LAMONEDA L., JUÁREZ R., SÁNCHEZ-SÁNCHEZ F., Dissection of solutions in cooperative game theory using representation techniques, Int. J. Game Theory, 2007, 35 (3), 395–426.
• [5] SÁNCHEZ-PÉREZ J., A decomposition for the space of games with externalities, Int. J. Game Theory, 2017, 46 (1), 205–233.
• [6] JACKSON M., Allocation rules for network games, Games Econ. Behav., 2005, 51, 128–154.
• [7] JACKSON M., WOLINSKY A., A strategic model of social and economic networks, J. Econ. Theory, 1996, 71, 44–74.
• [8] MYERSON R., Graphs and cooperation in games, Math. Oper. Res., 1977, 2 (3), 225–229.
• [9] SHAPLEY L., A value for n-person games, [In:] A.W. Tucker, R.D. Luce (Eds.), Contribution to the Theory of Games, Ann. Math. Studies, Princeton University Press, Princeton 1953, 307–317.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).