Three methods to share joint costs or surplus.

*(English)*Zbl 1016.91056Summary: We study cost sharing methods with variable demands of heterogeneous goods, additive in the cost function and meeting the dummy axiom. We consider four axioms: Scale Invariance (SI); Demand Monotonicity (DM); Upper Bound for Homogeneous goods (UBH) placing a natural cap on cost shares when goods are homogeneous; Average Cost Pricing for Homogeneous goods (ACPH). The random order values based on stand alone costs are characterized by SI and DM. Serial costsharing, by DM and UBH; the Aumann-Shapley pricing method, by SI and ACPH. No other combination of the four axioms is compatible with additivity and dummy.

##### MSC:

91B32 | Resource and cost allocation (including fair division, apportionment, etc.) |

91B18 | Public goods |

91B24 | Microeconomic theory (price theory and economic markets) |

PDF
BibTeX
XML
Cite

\textit{E. Friedman} and \textit{H. Moulin}, J. Econ. Theory 87, No. 2, 275--312 (1999; Zbl 1016.91056)

Full Text:
DOI

##### References:

[1] | Aczel, J., Functional equations and their applications, (1996), Academic Press New York |

[2] | Alchian, A.; Demsetz, H., Production, information costs and economic organization, Amer. econ. rev., 62, 77-95, (1972) |

[3] | Banker, R., Equity considerations in traditional full cost allocation practices: an axiomatic perspective, () |

[4] | Billera, L.; Heath, D., Allocation of shared costs: A set of axioms yielding a unique procedure, Math. oper. res., 7, 32-39, (1982) · Zbl 0509.90009 |

[5] | Billera, L.; Heath, D.; Raanan, J., Internal telephone billing rates: A novel application of non atomic game theory, Oper. res., 26, 956-965, (1978) · Zbl 0417.90059 |

[6] | Champsaur, P., How to share the cost of a public good?, Int. J. game theory, 4, 113-129, (1975) · Zbl 0318.90012 |

[7] | Chun, Y., The proportional solution for rights problems, Math. soc. sci., 15, 231-246, (1988) · Zbl 0657.92020 |

[8] | Clarke, D.; Shenker, S.; Zhang, L., Supporting real-time applications in an integrated services packet network: architecture and mechanism, Comput. comm. rev., 22, 14-26, (1992) |

[9] | Coffman, E.; Mitrani, I., A characterization of waiting time performance realizable by single server queue, Oper. res., 28, (1980) · Zbl 0451.90059 |

[10] | Conway, J., A course in functional analysis, (1985), Springer-Verlag New York · Zbl 0558.46001 |

[11] | Deutsch, M., Equity, equality and need, J. soc. issues, 31, 137-149, (1975) |

[12] | E. J. Friedman, Paths and consistency in additive cost sharing, mimeo, Rutgers University, 1998. |

[13] | O. Haimanko, Partially symmetric values, mimeo, Hebrew University, Jerusalem, 1998. |

[14] | Henriet, D.; Moulin, H., Traffic based cost allocation in a network, RAND J. econ., 27, 332-345, (1996) |

[15] | S. Herzog, S. Shenker, and, D. Estrin, Sharing the cost of multicast trees: An axiomatic analysis, mimeo, University of Southern California, 1995. |

[16] | Homans, G., Social behavior, its elementary forms, (1961), Harcourt, Brace and World New York |

[17] | Israelsen, D., Collectives, communes, and incentives, J. compar. econ., 4, 99-124, (1980) |

[18] | Khmelnitskaya, A., Marginalist and efficient values for TU games, Math. soc. sci., (1999) · Zbl 0941.91010 |

[19] | Kleinrock, L., Queueing systems, (1975), Wiley New York · Zbl 0334.60045 |

[20] | M. Koster, S. Tijs, and, P. Borm, Serial cost sharing methods for multi-commodity situations, mimeo, Tilbury University, 1996. |

[21] | Laffont, J.J.; Tirole, J., A theory of incentives in procurement and regulation, (1993), MIT Press Boston |

[22] | J. Lima, M. Pereira, and J. Pereira, An integrated framework for cost allocation in a multi-owned transmission system, IEEE Trans. Power Syst.101995, 971-977. |

[23] | Loehman, E.; Whinston, A., An axiomatic approach to cost allocation for public investment, Public finance quart., 2, 236-251, (1974) |

[24] | McLean, R.; Sharkey, W., Probabilistic value pricing, Math. oper. res., 43, 73-95, (1996) |

[25] | McLean, R.; Sharkey, W., Weighted aumann – shapley pricing, Int. J. game theory, 27, 511-524, (1998) · Zbl 0954.91020 |

[26] | Mas-Colell, A., Remarks on the game theoretic analysis of a simple distribution of surplus problem, Int. J. game theory, 9, 125-140, (1980) · Zbl 0476.90011 |

[27] | Mirman, L.; Tauman, Y., Demand compatible equitable cost sharing prices, Math. oper. res., 7, 40-56, (1982) · Zbl 0496.90016 |

[28] | Moulin, H., Equal or proportional division of a surplus, and other methods, Int. J. game theory, 16, 161-186, (1987) · Zbl 0631.90093 |

[29] | Moulin, H., Cooperative microeconomics, (1995), Princeton University Press Princeton |

[30] | Moulin, H., On additive methods to share joint costs, Japanese econ. rev., 46, 303-332, (1995) |

[31] | Moulin, H., Incremental cost sharing: characterization by group strategyproofness, Soc. choice welfare, 16, 279-320, (1999) · Zbl 1066.91502 |

[32] | Moulin, H.; Shenker, S., Serial cost sharing, Econometrica, 60, 1009-1037, (1992) · Zbl 0766.90013 |

[33] | Moulin, H.; Shenker, S., Average cost pricing versus serial cost sharing: an axiomatic comparison, J. econ. theory, 64, 178-201, (1994) · Zbl 0811.90008 |

[34] | Moulin, H.; Shenker, S., Distributive and additive costsharing of an homogeneous good, Games econ. behav., 27, 299-330, (1999) · Zbl 0957.91058 |

[35] | Phelps, R., Integral representations for elements of convex sets, (), 115-157 |

[36] | Rawls, J., A theory of justice, (1971), Harvard University Press Cambridge |

[37] | J. Redekop, Conditions for monotonicity of Aumann-Shapley pricing, mimeo, University of Waterloo, Ontario, 1996. |

[38] | J. Roemer, A public ownership resolution of the tragedy of the commons, mimeo, University of California, Davis, 1988. |

[39] | Roemer, J., Theories of distributive justice, (1996), Harvard University Press Cambridge |

[40] | Rudin, W., Principles of mathematical analysis, (1953), McGraw-Hill New York · Zbl 0052.05301 |

[41] | Scarf, H., Notes on the core of a productive economy, () · Zbl 0666.90017 |

[42] | Sen, A., Labour allocation in a cooperative enterprise, Rev. econ. stud., 33, 361-371, (1966) |

[43] | Shapley, L., A value for n-person games, () · Zbl 0050.14404 |

[44] | Shenker, S., Making greed work in networks: A game-theoretic analysis of gateway service disciplines, IEEE/ACM trans. networking, 3, 819-831, (1995) |

[45] | Shenker, S., Efficient network allocations with selfish users, () |

[46] | S. Shenker, On the strategyproof and smooth allocation of private goods in production economies, mimeo, PARC, Xerox Corporation, Palo Alto, CA, 1992. |

[47] | Shubik, M., Incentives, decentralized control, the assignment of joint costs and internal pricing, Manage. sci., 8, 325-343, (1962) · Zbl 0995.90578 |

[48] | Shubik, M., Game theory in the social sciences, (1982), MIT Press Cambridge · Zbl 0903.90179 |

[49] | Sprumont, Y., Ordinal cost sharing, J. econ. theory, 81, 126-162, (1998) · Zbl 0910.90277 |

[50] | Y. Sprumont, Coherent cost-sharing rules, mimeo, Université de Montréal, 1998. |

[51] | Y. Sprumont, and, Y. Wang, Ordinal additive cost sharing methods must be random order values, mimeo, Université de Montréal, 1996. |

[52] | Y. Sprumont, and, Y. T. Wang, A note on measurement invariance in discrete cost sharing problems, mimeo, Université de Montréal, 1996. |

[53] | Y. Sprumont, and, Y. T. Wang, A characterization of the Aumann-Shapley method in the discrete cost sharing model, mimeo, Université de Montréal, 1998. |

[54] | Thomas, A., A behavioral analysis of joint cost allocation and transfer pricing, Arthur Anderson and company lectures series, (1977), Stipes |

[55] | Wang, Y.T., The additivity and dummy axioms in the discrete cost sharing model, Econ. lett., (1999) · Zbl 0971.91509 |

[56] | Weber, R., Probabilistic values for games, () · Zbl 0707.90100 |

[57] | Young, H.P., Monotonicity in cooperative games, Int. J. game theory, 13, 65-72, (1985) · Zbl 0569.90106 |

[58] | Young, H.P., Producer incentives in cost allocation, Econometrica, 53, 757-765, (1985) · Zbl 0564.90003 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.