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Gradualism and Irreversibility


  • Ben Lockwood
  • Jonathan P. Thomas


This paper considers a class of two-player dynamic games in which each player controls a one-dimensional action variable, interpreted as a level of cooperation. The dynamics are due to an irreversibility constraint: neither player can ever reduce his cooperation level. Payoffs are decreasing in one's own action, increasing in one's opponent's action. We characterize efficient symmetric equilibrium action paths; actions rise gradually over time and converge, when payoffs are smooth, to a level strictly below the one-shot efficient level, no matter how little discounting takes place. The analysis is extended to incorporate sequential moves and asymmetric equilibria. Copyright 2002, Wiley-Blackwell.

Suggested Citation

  • Ben Lockwood & Jonathan P. Thomas, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 339-356.
  • Handle: RePEc:oup:restud:v:69:y:2002:i:2:p:339-356

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    References listed on IDEAS

    1. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
    2. Anat R. Admati & Motty Perry, 1991. "Joint Projects without Commitment," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 259-276.
    3. Pankaj Ghemawat & Barry Nalebuff, 1990. "The Devolution of Declining Industries," The Quarterly Journal of Economics, Oxford University Press, vol. 105(1), pages 167-186.
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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods


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