Gradualism and Irreversibility

CSGR Working Paper No. 28/99

35 Pages Posted: 27 Sep 1999

See all articles by Ben Lockwood

Ben Lockwood

University of Warwick - Department of Economics; Centre for Economic Policy Research (CEPR); CESifo (Center for Economic Studies and Ifo Institute)

Jonathan Thomas

University of Edinburgh - Economics; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: May 1999

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.

JEL Classification: C73, H41

Suggested Citation

Lockwood, Ben and Thomas, Jonathan P., Gradualism and Irreversibility (May 1999). CSGR Working Paper No. 28/99, Available at SSRN: https://ssrn.com/abstract=165796 or http://dx.doi.org/10.2139/ssrn.165796

Ben Lockwood (Contact Author)

University of Warwick - Department of Economics ( email )

Coventry CV4 7AL
United Kingdom
+44 24 7652 8906 (Phone)
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Centre for Economic Policy Research (CEPR)

London
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CESifo (Center for Economic Studies and Ifo Institute)

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Munich, DE-81679
Germany

Jonathan P. Thomas (Contact Author)

University of Edinburgh - Economics ( email )

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Edinburgh, EH8 9JY, Scotland
United Kingdom
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+44 131 650 4514 (Fax)

HOME PAGE: http://www.st-andrews.ac.uk/~jpt/

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

HOME PAGE: http://www.cesifo.de