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 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.
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Bibliographic InfoPaper provided by Centre for the Study of Globalisation and Regionalisation (CSGR), University of Warwick in its series CSGR Working papers series with number 28/99.
Date of creation: May 1999
Date of revision:
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Postal: Centre for the Study of Globalisation and Regionalisation (CSGR) University of Warwick Coventry CV4 7AL, U.K.
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Cooperation; repeated games; gradualism; irreversibility; public goods.;
Other versions of this item:
- Lockwood, Ben & Thomas, Jonathan P, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Wiley Blackwell, vol. 69(2), pages 339-56, April.
- Ben Lockwood & Jonathan P. Thomas, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 339-356.
- Ben Lockwood & Jonathan P. Thomas, 1999. "Gradualism and Irreversibility," Discussion Paper Series, Department of Economics 199909, Department of Economics, University of St. Andrews.
- Lockwood, B. & Thomas, J.P., 1999. "Gradualism and Irreversibility," The Warwick Economics Research Paper Series (TWERPS) 525, University of Warwick, Department of Economics.
- 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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- 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.
- Fershtman, Chaim & Nitzan, Shmuel, 1991.
"Dynamic voluntary provision of public goods,"
European Economic Review,
Elsevier, vol. 35(5), pages 1057-1067, July.
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