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The Tragedy of the Commons Revisited

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  • John M. Hartwick

Abstract

We formulate the Malthus-Hardin tragedy of the commons as a special case of dynamic game between "tribes". At each date a member of a tribe desires more newborns of her/his type and more current consumption, harvested from the commons. Equilibrium in the dynamic game yields steady state level of per capita consumption for each person and a steady population level for each tribe (births equal deaths). We obtain four outcomes, depending on our assumptions about the discount rates of members of a tribe and about the mode of competition for "large populations" for each tribe. We compare Nash open loop and Nash feedback solutions with a quadratic current utility function and observe a larger populations under the feedback solution. The classic tragedy of the commons solution obtains as a special case of the open loop solution, one with an infinite rate of discount for players.

Suggested Citation

  • John M. Hartwick, 1992. "The Tragedy of the Commons Revisited," Working Papers 856, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:856
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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_856.pdf
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