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 and 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. MaschlerE. 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.

show all references

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. MaschlerE. 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.

[1]

Leon Petrosyan, David Yeung. Shapley value for differential network games: Theory and application. Journal of Dynamics and Games, 2021, 8 (2) : 151-166. doi: 10.3934/jdg.2020021

[2]

Yan-An Hwang, Yu-Hsien Liao. Reduction and dynamic approach for the multi-choice Shapley value. Journal of Industrial and Management Optimization, 2013, 9 (4) : 885-892. doi: 10.3934/jimo.2013.9.885

[3]

Jun Huang, Ying Peng, Ruwen Tan, Chunxiang Guo. Alliance strategy of construction and demolition waste recycling based on the modified shapley value under government regulation. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3183-3207. doi: 10.3934/jimo.2020113

[4]

Xue-Yan Wu, Zhi-Ping Fan, Bing-Bing Cao. Cost-sharing strategy for carbon emission reduction and sales effort: A nash game with government subsidy. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1999-2027. doi: 10.3934/jimo.2019040

[5]

Xiaomei Li, Renjing Liu, Zhongquan Hu, Jiamin Dong. Information sharing in two-tier supply chains considering cost reduction effort and information leakage. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021200

[6]

Jiaqin Wei, Danping Li, Yan Zeng. Robust optimal consumption-investment strategy with non-exponential discounting. Journal of Industrial and Management Optimization, 2020, 16 (1) : 207-230. doi: 10.3934/jimo.2018147

[7]

Chandan Pal, Somnath Pradhan. Zero-sum games for pure jump processes with risk-sensitive discounted cost criteria. Journal of Dynamics and Games, 2022, 9 (1) : 13-25. doi: 10.3934/jdg.2021020

[8]

Fabián Crocce, Ernesto Mordecki. A non-iterative algorithm for generalized pig games. Journal of Dynamics and Games, 2018, 5 (4) : 331-341. doi: 10.3934/jdg.2018020

[9]

Andrei Korobeinikov. Global properties of a general predator-prey model with non-symmetric attack and consumption rate. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1095-1103. doi: 10.3934/dcdsb.2010.14.1095

[10]

Vincent Choudri, Mathiyazhgan Venkatachalam, Sethuraman Panayappan. Production inventory model with deteriorating items, two rates of production cost and taking account of time value of money. Journal of Industrial and Management Optimization, 2016, 12 (3) : 1153-1172. doi: 10.3934/jimo.2016.12.1153

[11]

Zeyang Wang, Ovanes Petrosian. On class of non-transferable utility cooperative differential games with continuous updating. Journal of Dynamics and Games, 2020, 7 (4) : 291-302. doi: 10.3934/jdg.2020020

[12]

Alain Bensoussan, Jens Frehse, Jens Vogelgesang. Systems of Bellman equations to stochastic differential games with non-compact coupling. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1375-1389. doi: 10.3934/dcds.2010.27.1375

[13]

Siting Liu, Levon Nurbekyan. Splitting methods for a class of non-potential mean field games. Journal of Dynamics and Games, 2021, 8 (4) : 467-486. doi: 10.3934/jdg.2021014

[14]

Fabien Gensbittel, Miquel Oliu-Barton, Xavier Venel. Existence of the uniform value in zero-sum repeated games with a more informed controller. Journal of Dynamics and Games, 2014, 1 (3) : 411-445. doi: 10.3934/jdg.2014.1.411

[15]

Zuo Quan Xu, Fahuai Yi. An optimal consumption-investment model with constraint on consumption. Mathematical Control and Related Fields, 2016, 6 (3) : 517-534. doi: 10.3934/mcrf.2016014

[16]

Barbara Bianconi, Francesca Papalini. Non-autonomous boundary value problems on the real line. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 759-776. doi: 10.3934/dcds.2006.15.759

[17]

Corentin Audiard. On the non-homogeneous boundary value problem for Schrödinger equations. Discrete and Continuous Dynamical Systems, 2013, 33 (9) : 3861-3884. doi: 10.3934/dcds.2013.33.3861

[18]

Angelo Favini, Rabah Labbas, Stéphane Maingot, Maëlis Meisner. Boundary value problem for elliptic differential equations in non-commutative cases. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 4967-4990. doi: 10.3934/dcds.2013.33.4967

[19]

R.M. Brown, L.D. Gauthier. Inverse boundary value problems for polyharmonic operators with non-smooth coefficients. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022006

[20]

Shuhua Zhang, Longzhou Cao, Zuliang Lu. An EOQ inventory model for deteriorating items with controllable deterioration rate under stock-dependent demand rate and non-linear holding cost. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021156

 Impact Factor: 

Metrics

  • PDF downloads (201)
  • HTML views (298)
  • Cited by (3)

Other articles
by authors

[Back to Top]