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Gradualism and Irreversibility

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Author Info
Ben Lockwood (Warwick)
Jonathan Thomas

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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 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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Paper provided by Department of Economics, University of St. Andrews in its series Discussion Paper Series, Department of Economics with number 9909.

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Date of creation: Dec 1999
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Handle: RePEc:san:wpecon:9909

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  1. Admati, Anat R & Perry, Motty, 1991. "Joint Projects without Commitment," Review of Economic Studies, Blackwell Publishing, vol. 58(2), pages 259-76, April. [Downloadable!] (restricted)
  2. Ghemawat, Pankaj & Nalebuff, Barry, 1990. "The Devolution of Declining Industries," The Quarterly Journal of Economics, MIT Press, vol. 105(1), pages 167-86, February. [Downloadable!] (restricted)
  3. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July. [Downloadable!] (restricted)
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  2. Ben Zissimos, 2006. "The GATT and Gradualism," Working Papers 0619, Department of Economics, Vanderbilt University. [Downloadable!]
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  3. Francesca Flamini, 2007. "Long-run Negotiations withDynamic Accumulation," Working Papers 2007_23, Department of Economics, University of Glasgow. [Downloadable!]
  4. Steven A. Matthews, 2006. "Smooth Monotone Contribution Games," PIER Working Paper Archive 06-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
  5. Sergei Guriev & Dmitriy Kvasov, 2005. "Contracting on Time," American Economic Review, American Economic Association, vol. 95(5), pages 1369-1385, December. [Downloadable!] (restricted)
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  6. Yeon-Koo Che & Jozsef Sakovics, 2004. "A Dynamic Theory of Holdup," ESE Discussion Papers 74, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
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  7. Sophie Bade & Guillaume Haeringer & Ludovic Renou, 2006. "Bilateral Commitment," Working Papers 2006-07, University of Adelaide, School of Economics. [Downloadable!]
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  9. Guillermo Caruana & Liran Einav & Daniel Quint, 2004. "Multilateral Bargaining With Concession Costs," Working Papers wp2004_0415, CEMFI. [Downloadable!]
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