Impacts of boycotts concerning the Shapley value and extensions

Besner, Manfred (2022): Impacts of boycotts concerning the Shapley value and extensions. Published in: Economics Letters , Vol. 217, (August 2022): p. 110685.

Abstract

If a player boycotts another player, it means that the cooperation gains of all coalitions containing both players vanish. In the associated coalition function, both players are now disjointly productive with respect to each other. The disjointly productive players property states that a player's payoff does not change when another player who is disjointly productive to that player is removed from the game. We show that the Shapley value is the only TU-value that satisfies efficiency and the disjointly productive players property and for which the impact of a boycott is the same for the boycotting and the boycotted player. Analogous considerations are made for the proportional Shapley value and the class of (positively) weighted Shapley values.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cooperative game · (Weighted/proportional) Shapley value · Disjointly productive players · (Weighted/proportional) impacts of boycotts
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

References

Béal, S., Ferrières, S., Rémila, E., & Solal, P. (2018). The proportional Shapley value and applications. Games and Economic Behavior 108, 93–112.

Besner, M. (2016). Lösungskonzepte kooperativer Spiele mit Koalitionsstrukturen. Diplomarbeit, Fern-Universit¨at Hagen, Germany

Besner, M. (2019). Axiomatizations of the proportional Shapley value. Theory and Decision, 86(2), 161–183.

Besner, M. (2020). Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution. International Journal of Game Theory, 1–23.

Besner, M. (2022) Disjointly productive players and the Shapley value. Games and Economic Behavior 133, 109–114.

Casajus, A. (2021). Second-order productivity, second-order payoffs, and the Shapley value. Discrete Applied Mathematics, 304, 212–219.

Dragan, I. C. (1992). Multiweighted Shapley values and random order values. University of Texas at Arlington.

Grabisch, M., & Roubens, M. (1999). An axiomatic approach to the concept of interaction among players in cooperative games. International Journal of game theory, 28(4), 547–565.

Harsanyi, J. C. (1959). A bargaining model for cooperative n-person games. In: A. W. Tucker & R. D. Luce (Eds.), Contributions to the theory of games IV (325–355). Princeton NJ: Princeton University Press.

Hart, S., & Mas-Colell, A. (1989). Potential, value, and consistency. Econometrica: Journal of the Econometric Society, 589–614.

Kalai, E., & Samet, D. (1987). On weighted Shapley values. International Journal of Game Theory 16(3), 205–222.

Moriarity, S. (1975). Another approach to allocating joint costs. The Accounting Review, 50(4), 791–795.

Myerson, R. B. (1980). Conference structures and fair allocation rules. International Journal of Game Theory, 9(2), 169–182.

Nowak, A. S., & Radzik, T. (1995). On axiomatizations of the weighted Shapley values. Games and Economic Behavior, 8(2), 389–405.

Shapley, L. S. (1953a). Additive and non-additive set functions. Princeton University.

Shapley, L. S. (1953b). A value for n-person games. H. W. Kuhn/A. W. Tucker (eds.), Contributions to the Theory of Games, Vol. 2, Princeton University Press, Princeton, pp. 307–317.