Besner, Manfred (2017): Weighted Shapley levels values.
![Warning](/style/images/warning.png)
Preview |
PDF
MPRA_paper_82978.pdf Download (498kB) | Preview |
Abstract
This paper presents a collection of four different classes of weighted Shapley levels values. All classes contain generalisations of the weighted Shapley values to cooperative games with a level structure. The first class is an upgrade of the weighted Shapley levels value in Gómez-Rúa and Vidal-Puga (2011), who use the size of components as weights. The following classes contain payoff vectors from the Harsanyi set. Hence they satisfy the dummy axiom, in contrary to the values in the first class in general. The second class contains extensions of the McLean weighted coalition structure values (Dragan, 1992; Levy and McLean, 1989; McLean, 1991). The first two classes satisfy the level game property (the payoff to all players of a component sum up to the payoff to the component in a game where components are the players) and the last two classes meet a null player out property. As a special case, the first three classes include the Shapley levels value and the last class contains a new extension of the Shapley value.
Item Type: | MPRA Paper |
---|---|
Original Title: | Weighted Shapley levels values |
Language: | English |
Keywords: | Cooperative game; Level structure; (Weighted) Shapley (levels) value; Weighted proportionality; Harsanyi set; Dividends |
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: | 82978 |
Depositing User: | Manfred Besner |
Date Deposited: | 29 Nov 2017 14:34 |
Last Modified: | 29 Sep 2019 22:46 |
References: | Álvarez-Mozos, M., van den Brink, R., van der Laan, G., & Tejada, O. (2017). From hierarchies to levels: new solutions for games with hierarchical structure. International Journal of Game Theory, 1–25. Aumann, R.J., Drèze, J., 1974. Cooperative games with coalition structures. International Journal of Game Theory 3, 217–237. Besner, M. (2016). Lösungskonzepte kooperativer Spiele mit Koalitionsstrukturen, Master’s thesis, Fern-Universität Hagen (Germany). Béal, S., Ferrières, S., Rémila, E., & Solal, P. (2017). The proportional Shapley value and applications. Games and Economic Behavior. Calvo, E., Lasaga, J. J., & Winter, E. (1996). The principle of balanced contributions and hierarchies of cooperation, Mathematical Social Sciences, 31(3), 171–182. Casajus, A., & Huettner, F. (2008). Marginality is equivalent to coalitional strategic equivalence. Working paper. Casajus, A. (2010). Another characterization of the Owen value without the additivity axiom. Theory and decision, 69(4), 523–536. Casajus, A. (2017). Weakly balanced contributions and solutions for cooperative games. Operations Research Letters, 45, 616–619. Chun, Y. (1989). A new axiomatization of the Shapley value. Games and Economic Behavior 1(2), 119–130. Derks, J. J., & Haller, H. H. (1999). Null players out? Linear values for games with variable supports. International Game Theory Review, 1(3–4), 301–314. Derks, J., Haller, H., & Peters, H. (2000). The selectope for cooperative games. International Journal of Game Theory, 29(1), 23–38. Dragan, I. C. (1992). Multiweighted Shapley values and random order values. University of Texas at Arlington. Gangolly, J. S. (1981). On joint cost allocation: Independent cost proportional scheme (ICPS) and its properties. Journal of Accounting Research, 299–312. Gómez-Rúa, M., & Vidal-Puga, J. (2011). Balanced per capita contributions and level structure of cooperation. Top, 19(1), 167–176. Hammer, P. L., Peled, U. N., & Sorensen, S. (1977). Pseudo-boolean functions and game theory. I. Core elements and Shapley value. Cahiers du CERO, 19, 159–176. 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, 57(3) 589–614. Kalai, E., & Samet, D. (1987). On weighted Shapley values. International Journal of Game Theory 16(3), 205–222. Khmelnitskaya, A. B., & Yanovskaya, E. B. (2007). Owen coalitional value without additivity axiom. Mathematical Methods of Operations Research, 66(2), 255–261. Levy, A., & Mclean, R. P. (1989). Weighted coalition structure values. Games and Economic Behavior, 1(3), 234–249. McLean, R. P. (1991). Random order coalition structure values. International Journal of Game Theory, 20(2), 109–127. Myerson, R. B. (1980). Conference Structures and Fair Allocation Rules, International Journal of Game Theory, Volume 9, Issue 3, 169–182. Nowak, A. S., & Radzik, T. (1995). On axiomatizations of the weighted Shapley values. Games and Economic Behavior, 8(2), 389–405. Owen, G. (1977). Values of games with a priori unions. In Essays in Mathematical Economics and Game Theory, Springer, Berlin Heidelberg, 76–88. 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. 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. Vasil’ev, V. A. (1978). Support function of the core of a convex game. Optimizacija Vyp, 21, 30-35. Vidal-Puga, J. (2012). The Harsanyi paradox and the ”right to talk” in bargaining among coalitions. Mathematical Social Sciences, 64(3), 214–224. Winter, E. (1989). A value for cooperative games with levels structure of cooperation. International Journal of Game Theory, 18(2), 227–240. Winter, E. (2002). The Shapley value. In: Aumann, R. J., Hart, S. (Eds.). Handbook of Game Theory, with Economic Applications, Vol. 3. Elsevier, 2025–2054. Young, H. P. (1985). Monotonic solutions of Cooperative Games. International Journal of Game Theory, 14(2), 65–72. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/82978 |
Available Versions of this Item
- Weighted Shapley levels values. (deposited 29 Nov 2017 14:34) [Currently Displayed]