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Gradualism and Irreversibility

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  • Ben Lockwood
  • Jonathan P. Thomas

Abstract

This paper considers a class of two-player dynamic games in which each player controls a one-dimensional variable which we interpret as a level of cooperation. In the base model, there is an irreversibility constraint stating that this variable can never be reduced, only increased. It otherwise satisfies the usual discounted repeated game assumptions. Under certain restrictions on the payoff function, which make the stage game resemble a continuous version of the Prisoners' Dilemma, we characterize efficient symmetric equilibria, and show that cooperation levels exhibit gradualism and converge to a level strictly below the one-shot efficient level: the irreversibility induces a steady-state as well as a dynamic inefficiency. As players become very patient, however, payoffs converge to (though never attain) the efficient level. We also show that a related model in which an irreversibility arises through players choosing an incremental variable, such as investment, can be transformed into the base model with similar results. Applications to a public goods sequential contribution model and a model of capacity reduction in a declining industry are discussed. The analysis is extended to incorporate partial reversibility, asymmetric equilibria, and sequential moves.

Suggested Citation

  • Ben Lockwood & Jonathan P. Thomas, 1999. "Gradualism and Irreversibility," CSGR Working papers series 28/99, Centre for the Study of Globalisation and Regionalisation (CSGR), University of Warwick.
  • Handle: RePEc:wck:wckewp:28/99
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    References listed on IDEAS

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    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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    More about this item

    Keywords

    Cooperation; repeated games; gradualism; irreversibility; public goods.;

    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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