# American Institute of Mathematical Sciences

January 2018, 5(1): 31-39. doi: 10.3934/jdg.2018004

## A solution for discrete cost sharing problems with non rival consumption

 1 Universidade de Vigo, Statistics and Operations Research Program; Vigo, Spain 2 UASLP, School of Economics; San Luis Potosí, SLP, Mexico

* Corresponding author: adnavarro@uvigo.es

Received  April 2017 Revised  September 2017 Published  January 2018

Fund Project: The authors acknowledge support from CONACyT grant 240229.

In this paper we show several results regarding to the classical cost sharing problem when each agent requires a set of services but they can share the benefits of one unit of each service, i.e. there is non rival consumption. Specifically, we show a characterized solution for this problem, mainly adapting the well-known axioms that characterize the Shapley value for TU-games into our context. Finally, we present some additional properties that the shown solution satisfy.

Citation: Adriana Navarro-Ramos, William Olvera-Lopez. A solution for discrete cost sharing problems with non rival consumption. Journal of Dynamics & Games, 2018, 5 (1) : 31-39. doi: 10.3934/jdg.2018004
##### References:
 [1] J. Macias-Ponce and W. Olvera-Lopez, A characterization of a solution based on prices for a discrete cost sharing problem, Economics Bulletin, 33 (2013), 1429-1437. [2] M. Maschler, E. Solan and S. Zamir, Game Theory, 1 $^{st}$ edition, Cambridge University Press, 2013. doi: 10.1017/CBO9780511794216. [3] H. Moulin, On additive methods to share joint costs, The Japanese Economic Review, 46 (1995), 303-332. doi: 10.1111/j.1468-5876.1995.tb00024.x. [4] D. Samet and Y. Tauman, The determination of marginal cost prices under a set of axioms, Econometrica, 50 (1982), 895-909. doi: 10.2307/1912768. [5] L. S. Shapley, A value for n-person games, in Contributions to the Theory of Games. Annals of Mathematical Studies (eds. Kuhn, H. W. ; Tucker, A. W. ), Princeton University Press, 28 (1953), 307-317. [6] Y. Sprumont, On the discrete version of the Aumann-Shapley cost sharing method, Econometrica, 73 (2005), 1693-1712. doi: 10.1111/j.1468-0262.2005.00633.x.

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##### References:
 [1] J. Macias-Ponce and W. Olvera-Lopez, A characterization of a solution based on prices for a discrete cost sharing problem, Economics Bulletin, 33 (2013), 1429-1437. [2] M. Maschler, E. Solan and S. Zamir, Game Theory, 1 $^{st}$ edition, Cambridge University Press, 2013. doi: 10.1017/CBO9780511794216. [3] H. Moulin, On additive methods to share joint costs, The Japanese Economic Review, 46 (1995), 303-332. doi: 10.1111/j.1468-5876.1995.tb00024.x. [4] D. Samet and Y. Tauman, The determination of marginal cost prices under a set of axioms, Econometrica, 50 (1982), 895-909. doi: 10.2307/1912768. [5] L. S. Shapley, A value for n-person games, in Contributions to the Theory of Games. Annals of Mathematical Studies (eds. Kuhn, H. W. ; Tucker, A. W. ), Princeton University Press, 28 (1953), 307-317. [6] Y. Sprumont, On the discrete version of the Aumann-Shapley cost sharing method, Econometrica, 73 (2005), 1693-1712. doi: 10.1111/j.1468-0262.2005.00633.x.
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