A Characterization of the Shapley Value for Cooperative Games

Hsiao, Chih-Ru and Chiou, Wen-Lin (2009): A Characterization of the Shapley Value for Cooperative Games.

Abstract

Motivated by a case of discrimination against some particular players happened in the real world, we define the partially consistent property of the solutions for cooperative games and use the property to characterize the Shapley value. This is different from the characterization of the Shapley value by applying the consistency property proposed by Hart and Mas-Colell.

• Item Type: MPRA Paper
• Language: English
• Keywords: Shapley value; Reduced Game; Partialy Consistent
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory

References

1. Hart, S and Mas-Colell (1989), Potential, value, and Consistency. Econometrica, vol. 57, No. 3, pp. 589~614.

2. Chang, C and Kan CY (1992),The kernel, the bargaining set and the reduced game. 21 International Journal of Game Theory, pp. 75-83.

3. Hsiao CR (1995), A Note on Non-essential Players in Multi-Choice Cooperative Games. Games and Economic Behavior, 8(1995), 424-432.

4. Hsiao CR and Liao YS (2008), The potential and consistency property for multi-choice Shapley value. Taiwanese Journal of Mathematics, 12 (2): 545-559.

5. Shapley LS, A Value for n-person Game.In: Kuhn HW, Tucker AW(eds.) Contributions to the Theory of Games II, Annals of Mathematics Studies 28, Princeton University Press, Princeton, 307-317.

6. Roth, A.: {\sl The Shapley Value. } Essays in honor of L.S.Shapley, Edited by A. Roth, Cambridge University Press, 1988.