Gradualism and Irreversibility
AbstractThis 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 quilibria. Efficient cooperation levels exhibit gradualism and converge, when payoffs are smooth, 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. An application to a public goods sequential contribution model is discussed. The analysis is extended to incorporate sequential moves, asymmetric equilibria and partial reversibility.
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Bibliographic InfoPaper provided by Department of Economics, University of St. Andrews in its series Discussion Paper Series, Department of Economics with number 199909.
Date of creation: 15 Dec 1999
Date of revision:
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Other versions of this item:
- Ben Lockwood & Jonathan P. Thomas, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 339-356.
- Lockwood, Ben & Thomas, Jonathan P, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Wiley Blackwell, vol. 69(2), pages 339-56, April.
- Lockwood, B. & Thomas, J.P., 1999. "Gradualism and Irreversibility," The Warwick Economics Research Paper Series (TWERPS) 525, University of Warwick, Department of Economics.
- 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.
- Lockwood, B. & Thomas, J.P., 1999. "Gradualism and Irreversibility," The Warwick Economics Research Paper Series (TWERPS) 550, University of Warwick, Department of Economics.
- 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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"Dynamic voluntary provision of public goods,"
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- Admati, Anat R & Perry, Motty, 1991. "Joint Projects without Commitment," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 259-76, April.
- Ghemawat, Pankaj & Nalebuff, Barry, 1990. "The Devolution of Declining Industries," The Quarterly Journal of Economics, MIT Press, vol. 105(1), pages 167-86, February.
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