Economic design

, Volume 2, Issue 1, pp 399–421 | Cite as

Two versions of the tragedy of the commons

  • Hervé Moulin
  • Alison Watts
Article

Abstract

The commons are a one input-one output production process with increasing marginal cost. In the everage return game, each agent chooses his input contribution and total output is shared in proportion to individual contributions. In the average cost game, each agent chooses his output share and total input cost is shared in proportion to individual demands. The tragedy is that the non cooperative equilibrium results in inefficient overutilization of the technology. We prove formally the tragedy when individual preferences are convex and both goods are normal. This result has not been proved previously on such a general preference domain. We also show that overutilization is less severe in the average cost game than in the average return game.

JEL classification

D62 D72 

Keywords

Externalities Tragedy of the commons Cost sharing Surplus sharing Average cost Average return 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bar-Hillel, M. and M. Yaari, 1993, Judgments of justice, in: B. Mellers and J. Baron, eds. Psychological Perspectives on Justice, ch. 4. (Cambridge University Press, Cambridge) 55–84.Google Scholar
  2. Billera, L. and D. Health, 1982, Allocations of shared costs: A set of axioms yielding a unique procedure, Mathematics of Operations Research 7, 32–39.Google Scholar
  3. Bryant, J., 1987. The paradox of thrift. liquidity preference and animal spirits, Econometrica 55(5), 1231–1235.CrossRefGoogle Scholar
  4. Case, J.H., 1979, Economics and the Competitive Process, ch.2 (New York University Press, New York).Google Scholar
  5. Dasgupta, P. and G. Heal, 1979, Economics theory and exhaustible resources (Cambridge University Press, Cambridge).Google Scholar
  6. Hardin, G., 1968. The tragedy of the commons, Science 162, 1243–1248.Google Scholar
  7. Israelsen, L.D., 1980, Collectives, Communes and Incentives, Journal of Comparative Economics 4, 99–124.CrossRefGoogle Scholar
  8. Kitch, E.W., 1977, The nature and function of the patent system, The Journal of Law and Economics 20, 265–290.CrossRefGoogle Scholar
  9. Loury, G.C., 1979, Market structure and innovation: A reformulation. Quarterly Journal of Economics 93(3), 395–409.CrossRefGoogle Scholar
  10. Moulin, H., 1995, Cooperative Microeconomics, ch. 6 (Princeton University Press).Google Scholar
  11. Moulin, H. and S. Shenker, 1992, Serial cost sharing, Econometrica 60, 1009–1037.CrossRefGoogle Scholar
  12. Moulin, H. and S. Shenker, 1994, Average cost pricing versus serial cost sharing: an axiomatic comparison, Journal of Economic Theory 64(1), 178–201.CrossRefGoogle Scholar
  13. Ostrom, E., 1991, Governing the Commons (Cambridge University Press, New York).Google Scholar
  14. Posner, R.A., 1992, Economic Analysis of Law, ch. 3, 4th Ed. (Little, Brown and Company, Boston).Google Scholar
  15. Riley, J.G., 1991, Asymmetric Contests, Mimeo, UCLA.Google Scholar
  16. Roemer, J.E., 1989, A public ownership resolution of the tragedy of the commons, Social Philosophy and Politics 6(2), 74–92.CrossRefGoogle Scholar
  17. Romano, R., 1988, Oligopolistic competition for market share via voluntary excess supply, International Journal of Industrial Organization 6, 447–468.CrossRefGoogle Scholar
  18. Shenker, S., 1990, Making Greed Work in Networks: a game theoretic analysis of gateway service disciplines, Mimeo, Xerox Palo Alto Research Center.Google Scholar
  19. Shubik M., 1962, Incentives, decentralized control, the assignment of joint costs and internal pricing, Management Science, 325–343.Google Scholar
  20. Tullock, G., 1980, Efficient rent seeking, in: J. Buchanan, R. Tollison and G. Tullock, eds., Toward a Theory of the Rent Seeking Society (Texas A&M Press).Google Scholar
  21. Watts, A., 1996a, On the uniqueness of equilibrium in Cournot oligopoly and other games, Games and Economic Behavior 13, 269–285.CrossRefGoogle Scholar
  22. Watts, A., 1996b, Uniqueness of Equilibrium in Cost Sharing Games, Mimeo, Vanderbilt University.Google Scholar

Copyright information

© Elsevier Science B.V. 1996

Authors and Affiliations

  • Hervé Moulin
    • 1
  • Alison Watts
    • 2
  1. 1.Department of EconomicsDuke UniversityDurhamUSA
  2. 2.Department of EconomicsVanderbilt UniversityNashvilleUSA

Personalised recommendations