Besner, Manfred (2017): Axiomatizations of the proportional Shapley value. Published in: Theory and Decision , Vol. 86, No. 2 (31 January 2019): pp. 161183.
This is the latest version of this item.

PDF
MPRA_paper_89193.pdf Download (417kB)  Preview 
Abstract
We provide new axiomatic characterizations of the proportional Shapley value, a weighted TUvalue with the worths of the singletons as weights. The presented characterizations are proportional counterparts to the famous characterizations of the Shapley value by Shapley (1953b) and Young (1985a). We introduce two new axioms, called proportionality and player splitting respectively. Each of them makes a main difference between the proportional Shapley value and the Shapley value. If the standalone worths are plausible weights, the proportional Shapley value is a convincing alternative to the Shapley value, for example in cost allocation. Especially the player splitting property, which states that the players’ payoffs do not change if another player splits into two new players who have the same impact to the game as the original player, justifies the use of the proportional Shapley value in many economic situations.
Item Type:  MPRA Paper 

Original Title:  Axiomatizations of the proportional Shapley value 
Language:  English 
Keywords:  Cost allocation; Dividends; Proportional Shapley value; (Weighted) Shapley value; Proportionality; Player splitting 
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 
Item ID:  93439 
Depositing User:  Manfred Besner 
Date Deposited:  22 Apr 2019 18:46 
Last Modified:  30 Sep 2019 22:13 
References:  Amer, R., Carreras, F., & Magana, A. (2007). Two Main Methods for Utility Sharing in Joint Business: A Discussion. Journal of Mathematics and Statistics 3(1), 28–35. Banker, R. D. (1981). Equity Considerations in Traditional Full Cost Allocation Practices: An Axiomatic Perspective. CarnegieMellon University. Barton, T. L. (1988). Intuitive choice of cooperative sharing mechanisms for joint cost savings: Some empirical results. Abacus, 24(2), 162–169. Béal, S., Ferrières, S., Remila, E., & Solal, P. (2016). The proportional Shapley value and applications. Games and Economic Behavior. Besner, M. (2016). Lösungskonzepte kooperativer Spiele mit Koalitionsstrukturen, Master’s thesis at the Chair of Discrete Mathematics, FernUniversität in Hagen. van den Brink, R., Levínský, R., & Zelený, M. (2015). On proper Shapley values for monotone TUgames. International Journal of Game Theory, 44(2), 449–471. Casajus, A., & Huettner, F. (2008). Marginality is equivalent to coalitional strategic equivalence. Working paper. Chun, Y. (1989). A new axiomatization of the Shapley value. Games and Economic Behavior 1(2), 119–130. Feldman, B. (1999). The proportional value of a cooperative game. Manuscript. Chicago: Scudder Kemper Investments. Gangolly, J. S. (1981). On joint cost allocation: Independent cost proportional scheme (ICPS) and its properties. Journal of Accounting Research, 299–312. Harsanyi, J. C. (1959). A bargaining model for cooperative nperson 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., & MasColell, A. (1989). Potential, value, and consistency. Econometrica, 57(3) 589–614. Kalai, E., & Samet, D. (1987). On weighted Shapley values. International Journal of Game Theory 16(3), 205–222. Leng, M., & Parlar, M. (2009). Allocation of cost savings in a threelevel supply chain with demand information sharing: A cooperativegame approach. Operations Research, 57(1), 200–213. 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, Volume 9, Issue 3, 169–182. von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton, NJ: Princeton Univ. Press. Nowak, A. S., & Radzik, T. (1995). On axiomatizations of the weighted Shapley values. Games and Economic Behavior, 8(2), 389–405. Ortmann, K. M. (2000). The proportional value for positive cooperative games. Mathematical Methods of Operations Research, 51(2), 235–248. Radzik, T. (2012). A new look at the role of players’ weights in the weighted Shapley value. European Journal of Operational Research, 223(2), 407–416. Roth, A. E., & Verrecchia, R. E. (1979). The Shapley value as applied to cost allocation: a reinterpretation. Journal of Accounting Research, 295–303. Shapley, L. S. (1953a). Additive and nonadditive set functions. Princeton University. Shapley, L. S. (1953b). A value for nperson games. H. W. Kuhn/A. W. Tucker (eds.), Contributions to the Theory of Games, Vol. 2, Princeton University Press, Princeton, pp. 307–317. Shubik, M. (1962). Incentives, decentralized control, the assignment of joint costs and internal pricing. Management science, 8(3), 325–343. Spinetto, R. D. (1975). Fairness in cost allocations and cooperative games. Decision Sciences, 6(3), 482–491. Thomas, A. L. (1969). The Allocation Problem in Financial Accounting TheoryStudies in Accounting Research No. 3. American Accounting Association, Evanston, Illinois. Thomas, A. L. (1974). The allocation problem in financial accounting theory (No. 9). American Accounting Association. Young, H. P. (1985a). Monotonic solutions of Cooperative Games. International Journal of Game Theory, 14(2), 65–72. Young, H. P. (1985b). Cost Allocation: Methods, Principles, Applications. North Holland Publishing Co.. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/93439 
Available Versions of this Item

Axiomatizations of the proportional Shapley value. (deposited 29 Nov 2017 14:28)

Axiomatizations of the proportional Shapley value. (deposited 30 Nov 2017 17:16)

Axiomatizations of the proportional Shapley value. (deposited 04 Dec 2017 14:24)

Axiomatizations of the proportional Shapley value. (deposited 26 Sep 2018 15:06)
 Axiomatizations of the proportional Shapley value. (deposited 22 Apr 2019 18:46) [Currently Displayed]

Axiomatizations of the proportional Shapley value. (deposited 26 Sep 2018 15:06)

Axiomatizations of the proportional Shapley value. (deposited 04 Dec 2017 14:24)

Axiomatizations of the proportional Shapley value. (deposited 30 Nov 2017 17:16)