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Cost sharing: Efficiency and implementation. (English) Zbl 0943.91042

Summary: We study environments where a production process is jointly shared by a finite group of agents. The social decision involves the determination of input contribution and output distribution. We define a competitive solution when there is decreasing-returns-to-scale which leads to a Pareto optimal outcome. Since there is a finite number of agents, the competitive solution is prone to manipulation. We constract a mechanism for which the set of Nash equilibria coincides with the set of competitive solution outcomes. We define a Marginal-Cost-Pricing Equilibrium (MCPE) solution for environments with increasing returns to scale. These solutions are Pareto optimal under certain conditions. We construct another mechanism that realizes the MCPE.

MSC:

91B32 Resource and cost allocation (including fair division, apportionment, etc.)
91B50 General equilibrium theory
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[1] Abreu, D.; Sen, A., Subgame perfect implementation: a necessary and almost sufficient condition, Journal of Economic Theory, 50, 285-299 (1990) · Zbl 0694.90010
[2] Abreu, D.; Sen, A., Virtual implementation in Nash equilibrium, Econometrica, 59, 997-1021 (1991) · Zbl 0732.90007
[3] Beato, P., The existence of marginal cost pricing equilibria with increasing returns, The Quarterly Journal of Economics, 89, 669-688 (1982) · Zbl 0493.90015
[4] Bonnisseau, J.-M.; Cornet, B., Existence of marginal cost pricing equilibria in economies with several nonconvex firms, Econometrica, 58, 661-682 (1990) · Zbl 0728.90016
[5] Brown, D., 1991. Equilibrium analysis with non-convex technologies. In: Hildenbrand, W., Sonnenschein, H. (Eds.), Handbook of Mathematical Economics, Vol. 4, Chap. 36. North-Holland, Amsterdam, pp. 1963-1995.; Brown, D., 1991. Equilibrium analysis with non-convex technologies. In: Hildenbrand, W., Sonnenschein, H. (Eds.), Handbook of Mathematical Economics, Vol. 4, Chap. 36. North-Holland, Amsterdam, pp. 1963-1995. · Zbl 0943.91514
[6] Calsamiglia, X., Decentralized resource allocation and increasing returns, Journal of Economic Theory, 14, 263-283 (1977) · Zbl 0358.90015
[7] Cornet, B., 1990. Marginal cost pricing and pareto optimality. In: Essays in honor of Edmond Malinvaud, Vol. 1. MIT Press, Cambridge, MA.; Cornet, B., 1990. Marginal cost pricing and pareto optimality. In: Essays in honor of Edmond Malinvaud, Vol. 1. MIT Press, Cambridge, MA.
[8] Dierker, E., When does Marginal Cost Pricing lead to Pareto-efficiency?, Zeitschrift für NationalÖkonomie, 5, 41-66 (1986)
[9] Hong, L., Nash implementation in production economies, Economic Theory, 5, 401-417 (1995) · Zbl 0835.90005
[10] Hurwicz, L., Outcome functions yielding Walrasian and Lindahl allocations at Nash equilibrium points, Review of Economic Studies, 46, 217-225 (1979) · Zbl 0417.90027
[11] Hurwicz, L., Maskin, E., Postlewaite, A., 1995. Feasible Nash implementation of social choice rules when the designer does not know endowments or production sets. In: Ledyard, J.O. (Ed.), The Economics of Information Decentralization: Complexity, Efficiency, and Stability. Kluwer Academic, Boston, pp. 367-433.; Hurwicz, L., Maskin, E., Postlewaite, A., 1995. Feasible Nash implementation of social choice rules when the designer does not know endowments or production sets. In: Ledyard, J.O. (Ed.), The Economics of Information Decentralization: Complexity, Efficiency, and Stability. Kluwer Academic, Boston, pp. 367-433.
[12] Kamiya, K., Existence and uniqueness of equilibria with increasing returns, Journal of Mathematical Economics, 17, 149-178 (1988) · Zbl 0662.90013
[13] Kamiya, K., On the survival assumption in marginal (cost) pricing, Journal of Mathematical Economics, 17, 261-274 (1988) · Zbl 0657.90009
[14] Mantel, R., Equilibrio con rendimiento crecientes a escala, Anales de la Asociation Argentine de Economia Politica, 1, 271-283 (1979)
[15] Matsushima, H., A new approach to the implementation problem, Journal of Economic Theory, 45, 128-144 (1988) · Zbl 0642.90011
[16] Moore, J.; Repullo, R., Subgame perfect implementation, Econometrica, 56, 1191-1220 (1988) · Zbl 0657.90005
[17] Moulin, H.; Shenker, S., Serial cost sharing, Econometrica, 60, 1009-1037 (1992) · Zbl 0766.90013
[18] Moulin, H.; Shenker, S., Average cost pricing versus serial cost sharing: an axiomatic approach, Journal of Economic Theory, 64, 178-201 (1994) · Zbl 0811.90008
[19] Moulin, H.; Watts, A., Two versions of the tragedy of the commons, Economic Design, 2, 399-421 (1997)
[20] Palfrey, T.; Srivastava, S., Nash implementation using undominated strategies, Econometrica, 59, 479-501 (1991) · Zbl 0734.90004
[21] Postlewaite, A.; Wettstein, D., Continuous and feasible implementation, Review of Economic Studies, 56, 603-612 (1989) · Zbl 0688.90013
[22] Quinzii, M., 1991. Efficiency of marginal cost pricing equilibria. In: Majundar, M. (Ed.), Equilibrium and Dynamics: Essays in Honour of David Gale, Chap. 14. St. Martin’s Press, New York, pp. 260-286.; Quinzii, M., 1991. Efficiency of marginal cost pricing equilibria. In: Majundar, M. (Ed.), Equilibrium and Dynamics: Essays in Honour of David Gale, Chap. 14. St. Martin’s Press, New York, pp. 260-286.
[23] Schmeidler, D., Walrasian analysis via strategic outcome functions, Econometrica, 48, 1585-1593 (1980) · Zbl 0457.90014
[24] Varian, H., A solution to the problem of externalities when agents are well informed, American Economic Review, 84, 1278-1293 (1994)
[25] Young, H.P., 1994. Cost allocation. In: Aumann, R.J., Hart, S. (Eds.), Handbook of Game Theory, Vol. 2, Chap. 36. North-Holland, Amsterdam, pp. 1193-1235.; Young, H.P., 1994. Cost allocation. In: Aumann, R.J., Hart, S. (Eds.), Handbook of Game Theory, Vol. 2, Chap. 36. North-Holland, Amsterdam, pp. 1193-1235. · Zbl 0925.90085
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