Prices in mixed cost allocation problems. (English) Zbl 1027.91045
The problem under consideration is the dividing of the cost of consumption of a finite number of goods, some of which are divisible and another indivisible. This cost allocation problem (cap) is reformulated as a cooperative game with transferable utility. The paper’s goal is an extension of the Aumann-Shapley price rule that was created for nonatomic games. Such games are corresponding to ca problems with divisible goods. The authors’ extension of the AS price rule on the mixed cap is based on the theory of mixed multilevel (on players participation) games considered by them earlier. The main results are a formula for a generalized AS price rule for mixed cap and seven axioms which are the characterization of the rule.
Reviewer: Vladimir Gorbunov (Ul’yanovsk)
MSC:
| 91B32 | Resource and cost allocation (including fair division, apportionment, etc.) |
| 91B24 | Microeconomic theory (price theory and economic markets) |
| 91A12 | Cooperative games |
References:
| [1] | Aumann, R. J.; Shapley, L. S., Values of Non-atomic Games (1974), Princeton Univ. Press: Princeton Univ. Press Princeton · Zbl 0311.90084 |
| [2] | Billera, L. J.; Heath, D. C., Allocation of Shared Costs: A Set of Axioms Yielding a Unique Procedure, Math. Op. Res., 7, 32-39 (1982) · Zbl 0509.90009 |
| [3] | Billera, L.; Heath, D.; Raanan, J., International Telephone Billing Rates: A Novel Application of Non-atomic Game Theory, Op. Res., 26, 956-965 (1978) · Zbl 0417.90059 |
| [4] | Calvo, E.; Santos, J. C., A Value for Multichoice Games, Math. Soc. Sci., 40, 341-354 (2000) · Zbl 0978.91006 |
| [5] | Calvo, E.; Santos, J. C., The Multilevel Value (1998), University of Basque Country |
| [6] | Friedman, E.; Moulin, H., Three Methods to Share Joint Costs or Surplus, J. Econ. Theory, 87, 275-312 (1999) · Zbl 1016.91056 |
| [7] | Hsiao, C.-R.; Raghavan, T. E.S., Shapley Value for Multichoice Cooperative Games (I), Games Econ. Behav., 5, 240-256 (1993) · Zbl 0795.90092 |
| [8] | Koster, M.; Tijs, S.; Borm, P., Serial Cost Sharing Methods for MultiCommodity Situations, Math, Soc. Sci., 36, 229-242 (1998) · Zbl 0936.91037 |
| [9] | Mirman, L. J.; Tauman, Y., Demand Compatible Equitable Cost Sharing Prices, Math. Op. Res., 7, 40-56 (1982) · Zbl 0496.90016 |
| [10] | Moulin, H., On Additive Methods to Share Joint Costs, Jap. Econ. Rev., 46, 303-332 (1995) |
| [11] | Moulin, H.; Shenker, S., Serial Cost Sharing, Econometrica, 60, 1009-1037 (1992) · Zbl 0766.90013 |
| [12] | Moulin, H.; Shenker, S., Average Cost Pricing Versus Serial Cost Sharing: An Axiomatic Comparison, J. Econ. Theory, 64, 178-201 (1994) · Zbl 0811.90008 |
| [13] | Nouweland, A.; Potters, J.; Tijs, S.; Zarzuelo, J. M., Cores and Related Solution Concepts for Multi-Choice Games, ZOR—Math. Meth. Op. Res., 41, 289-311 (1995) · Zbl 0837.90133 |
| [14] | Owen, G., Multilinear Extensions of Games, Manage. Sci., 18, 64-79 (1972) · Zbl 0239.90049 |
| [15] | Shapley, L. S., A Value for \(n\)-Person Games, Ann. Math. Stud., 28, 307-317 (1953) · Zbl 0050.14404 |
| [16] | Shubik, M., Incentives, Descentralized Control, the Assignment of Joint Costs and Internal Pricing, Manage. Sci., 8, 325-343 (1962) · Zbl 0995.90578 |
| [17] | Sprumont, Y., Ordinal Cost Sharing, J.Econ. Theory, 81, 126-162 (1998) · Zbl 0910.90277 |
| [18] | Sprumont, Y, and, Wang, Y. T. 1998, A Characterization of the Aumann-Shapley Method in the Discrete Cost Sharing Model, mimeo, Université de Montréal.; Sprumont, Y, and, Wang, Y. T. 1998, A Characterization of the Aumann-Shapley Method in the Discrete Cost Sharing Model, mimeo, Université de Montréal. |
| [19] | Tauman, Y., The Aumann-Shapley Prices: A Survey, (Roth, A., The Shapley Value (1988), Cambridge Univ. Press: Cambridge Univ. Press New York), 279-304 · Zbl 0708.90009 |
| [20] | Young, H. P., Cost Allocation, (Aumann, R. J.; Hart, S., Handbook of Game Theory With Economic Applications (1994), Elsevier Science: Elsevier Science Amsterdam), 1193-1235 · Zbl 0925.90085 |
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