Solutions for network games and symmetric group representations

• Authors: SÁNCHEZ-PÉREZ Joss
• Languages of publication: EN

Abstracts

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.

Keywords

EN

network games; axiomatic solutions; representation theory; symmetric group

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2019
• Volume: 29
• Issue: 4
• Pages: 95-123

Contributors

author

SÁNCHEZ-PÉREZ Joss

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

References

• 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.
• CRISMAN K., ORRISON M., Representation theory of the symmetric group in voting theory and game theory, Cont. Math., 2017, 685, 97–116.
• FULTON W., HARRIS J., Representation Theory. A first course, Springer-Verlag Graduate Texts in Mathematics, New York 1991, 129.
• 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.
• SÁNCHEZ-PÉREZ J., A decomposition for the space of games with externalities, Int. J. Game Theory, 2017, 46 (1), 205–233.
• JACKSON M., Allocation rules for network games, Games Econ. Behav., 2005, 51, 128–154.
• JACKSON M., WOLINSKY A., A strategic model of social and economic networks, J. Econ. Theory, 1996, 71, 44–74.
• MYERSON R., Graphs and cooperation in games, Math. Oper. Res., 1977, 2 (3), 225–229.
• 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.

Identifiers

DOI

10.37190/ord190405