Paths and consistency in additive cost sharing

Abstract.We provide a direct proof of a representation theorem for additive cost sharing methods as sums of path methods. Also, by directly considering the paths that generate some common additive cost sharing methods (Aumann-Shapley, Shapley Shubik, and Serial Cost) we show that they are consistent. These results follow directly from a simple sufficient condition for consistency: being generated by an associative path. We also introduce a new axiom, dummy consistency, which is quite mild. Using this, we also show that the Aumann-Shapley and Serial Cost methods are the unique (additive) consistent extension of their restriction on all two agent problems, while the Shapley-Shubik method has multiple consistent extensions but a unique anonymous scale invariant one.

[1]  W. Thomson.  Consistent Allocation Rules , 1996 .

[2]  H. Moulin.  Priority Rules and Other Asymmetric Rationing Methods , 2000 .

[3]  P. Billingsley,et al.  Probability and Measure , 1980 .

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

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

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

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

[8]  J. A. Smiley,et al.  Incentives , 2019, Handbook of Research Methods and Applications in Experimental Economics.

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

[10]  Eric J. Friedman,et al.  Strategic properties of heterogeneous serial cost sharing , 2002, Math. Soc. Sci..

[11]  Ori Haimanko.  Value theory without symmetry , 2000, Int. J. Game Theory.

[12]  和孝 牧野.  On the ζ-Potential , 1966 .

[13]  S. Hart,et al.  Potential, value, and consistency , 1989 .

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

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

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

[17]  H. Young.  Cost allocation : methods, principles, applications , 1985 .

[18]  Eric J. Friedman,et al.  Strong monotonicity in surplus sharing , 2004 .

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

[20]  William W. Sharkey,et al.  Potential, Consistency, and Cost Allocation Prices , 2004, Math. Oper. Res..

[21]  Scott Shenker,et al.  Analysis and simulation of a fair queueing algorithm , 1989, SIGCOMM 1989.

[22]  Eric J. Friedman,et al.  Three Methods to Share Joint Costs or Surplus , 1999 .

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

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

[25]  Dov Monderer,et al.  Potentials and Weighted Values of Nonatomic Games , 1997, Math. Oper. Res..

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

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

[28]  Eric J. Friedman,et al.  Optimization Based Characterizations of Cost Sharing Methods , 1999 .

[29]  Eric J. Friedman,et al.  Learning and Implementation on the Internet , 1997 .

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