Three Solutions to a Simple Commons Problem

Hervé Moulin

Professor, Department of Economics, Rice University, MS 22, P. O. Box 1892, Houston, TX 77251-1892, USA, Tel: +1-713-348-3532 moulin@rice.edu

JEL Classification : C71, D63, D78

Abstract

We compare the equity and incentive properties of three efficient solutions to a simple problem of cooperative production with binary demands for a homogeneous service, when marginal cost is either monotonically increasing or monotonically decreasing.

The solutions are the familiar competitive equilibrium with equal incomes, the Shapley value of the stand alone cooperative game, and the virtual price solution, applying the egalitarian equivalence idea to this particular model.

Keywords:

Cooperative production, No-envy, Shapley value, Tragedy of the commons

Acknowledgments

This paper prepared for the SJE-KISDI, International Symposium on Cost Allocation in Telecommunications, Seoul National University, June 9, 2001, Seoul, Korea. Also support from the NSF under grant SES 0096230 is gratefully acknowledged.

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