Three Methods to Share Joint Costs or Surplus

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 UB; the Aumann-Shapley pricing method, by SI and ACPH. No other combination of the four axioms is compatible with Additivity and Dummy.

[1]  H. Moulin,et al.  Serial Cost Sharing , 1992 .

[2]  Scott Shenker,et al.  Making greed work in networks: a game-theoretic analysis of switch service disciplines , 1995, TNET.

[3]  Scott Shenker,et al.  Efficient Network Allocations with Selfish Users , 1990, Performance.

[4]  H. Moulin.  Incremental cost sharing: Characterization by coalition strategy-proofness , 1999 .

[5]  G. C. Homans,et al.  Social Behavior: Its Elementary Forms. , 1975 .

[6]  M. Deutsch.  Equity, Equality, and Need: What Determines Which Value Will Be Used as the Basis of Distributive Justice? , 1975 .

[7]  John E. Roemer,et al.  A Public Ownership Resolution of the Tragedy of the Commons , 1989, Social Philosophy and Policy.

[8]  Werner Hildenbrand,et al.  Contributions to mathematical economics in honor of Gérard Debreu , 1986 .

[9]  Deborah Estrin,et al.  Sharing the “cost” of multicast trees: an axiomatic analysis , 1995, SIGCOMM '95.

[10]  William W. Sharkey,et al.  Probabilistic value pricing , 1996, Math. Methods Oper. Res..

[11]  Robert J. Weber,et al.  Probabilistic Values for Games , 1977 .

[12]  L. D. Israelseni.  Collectives, communes and incentives. , 1980 .

[13]  Studies in Functional Analysis , 1980 .

[14]  H. Demsetz,et al.  Production, Information Costs, and Economic Organization , 1975, IEEE Engineering Management Review.

[15]  H. Moulin.  Equal or proportional division of a surplus, and other methods , 1987 .

[16]  Edward G. Coffman,et al.  A Characterization of Waiting Time Performance Realizable by Single-Server Queues , 1980, Oper. Res..

[17]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .

[18]  Ori Haimanko.  Partially Symmetric Values , 2000, Math. Oper. Res..

[19]  Louis J. Billera,et al.  Internal Telephone Billing Rates - A Novel Application of Non-Atomic Game Theory , 1978, Oper. Res..

[20]  S. Wittevrongel,et al.  Queueing Systems , 2019, Introduction to Stochastic Processes and Simulation.

[21]  YunTong Wang.  The additivity and dummy axioms in the discrete cost sharing model , 1999 .

[22]  A. Khmelnitskaya.  Marginalist and efficient values for TU games , 1999 .

[23]  Scott Shenker,et al.  Supporting real-time applications in an Integrated Services Packet Network: architecture and mechanism , 1992, SIGCOMM '92.

[24]  H. Moulin.  Cooperative Microeconomics: A Game-Theoretic Introduction , 1995 .

[25]  Scott Shenker.  Making greed work in networks: a game-theoretic analysis of gateway service disciplines , 1990, SIGMETRICS '90.

[26]  J. Aczél.  ’Cheaper by the Dozen’: Twelve Functional Equations and their Applications to the ’Laws of Science’ and to Measurement in Economics , 1988 .

[27]  John Hof,et al.  4 – Joint Cost Allocation , 1993 .

[28]  William W. Sharkey,et al.  Weighted Aumann-Shapley pricing , 1998, Int. J. Game Theory.

[29]  Yves Sprumont.  Coherent Cost-Sharing Rules , 2000, Games Econ. Behav..

[30]  M. Pereira,et al.  An integrated framework for cost allocation in a multi-owned transmission system , 1995 .

[31]  M. Shubik.  Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing , 1962 .

[32]  R. Masson.  The Creation of Risk Aversion by Imperfect Capital Markets , 1972 .

[33]  Edward C. Rosenthal.  Monotonicity of the core and value in dynamic cooperative games , 1990 .

[34]  Stef Tijs,et al.  Serial cost sharing methods for multi-commodity situations , 1998 .

[35]  P. Champsaur,et al.  How to share the cost of a public good? , 1975 .

[36]  J. Laffont,et al.  A Theory of Incentives in Procurement and Regulation , 1993 .

[37]  Yair Tauman,et al.  Demand Compatible Equitable Cost Sharing Prices , 1982, Math. Oper. Res..

[38]  H. Young.  Producer Incentives in Cost Allocation , 1985 .

[39]  G. Homans,et al.  Social Behavior: Its Elementary Forms. , 1961 .

[40]  Amartya Sen,et al.  Labour Allocation in a Cooperative Enterprise , 1966 .

[41]  H. Young.  Monotonic solutions of cooperative games , 1985 .

[42]  Balancedness, nonemptiness of the core and the existence of a majority equilibrium , 1984 .

[43]  Hervé Moulin,et al.  Distributive and Additive Costsharing of an Homogeneous Good , 1999 .

[44]  A. Mas-Colell,et al.  Remarks on the game-theoretic analysis of a simple distribution of surplus problem , 1980 .

[45]  H. Moulin,et al.  Average Cost Pricing versus Serial Cost Sharing: An Axiomatic Comparison , 1994 .

[46]  Louis J. Billera,et al.  Allocation of Shared Costs: A Set of Axioms Yielding A Unique Procedure , 1982, Math. Oper. Res..

[47]  Yves Sprumont.  Ordinal Cost Sharing , 1998 .

[48]  Y. Chun.  The proportional solution for rights problems , 1988 .

[49]  Hervé Moulin,et al.  Traffic Based Cost Allocation in Network , 1996 .

[50]  Andrew B. Whinston,et al.  An Axiomatic Approach to Cost Allocation for Public Investment , 1974 .

[51]  J. Roemer.  Theories of Distributive Justice , 1997 .

[52]  Ki Hang Kim.  Game theory in the social sciences , 1986 .

[53]  W. Rudin.  Principles of mathematical analysis , 1964 .

[54]  D. Whittaker,et al.  A Course in Functional Analysis , 1991, The Mathematical Gazette.

[55]  Hervé Moulin,et al.  ON ADDITIVE METHODS TO SHARE JOINT COSTS , 1995 .