Lockwood, Ben and Thomas, Jonathan P. (1999) Gradualism and irreversibility. Working Paper. Coventry: University of Warwick, Department of Economics. Warwick economic research papers (No.550).

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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 equilibria, and show that 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. 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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Cooperation, Public goods, Prisoner's dilemma game, Games of strategy (Mathematics), Game theory
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Official Date:	April 1999
Dates:	Date Event April 1999 Published
Number:	No.550
Number of Pages:	38
Institution:	University of Warwick
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Economic and Social Research Council (Great Britain) (ESRC)
References:	[1] Admati, A. R. and M. Perry (1991) “Joint Projects without Commitment”, Review of Economic Studies, 58, 259-276. [2] Bagwell, K. and R.W. Staiger (1997) “GATT-Think”, mimeo, Columbia University. [3] Compte, C. and P. Jehiel (1998) “When Outside Options Force Concessions to be Gradual”, mimeo, C.E.R.A.S., Paris. [4] Fershtman, C. and S, Nitzan (1991) “Dynamic Voluntary Provision of Public Goods”, European Economic Review, 35, 1057-1067. [5] Gale, D. (1997) “Monotone Games”, mimeo, Department of Economics, New York University. [6] Ghemawat, P. and B. Nalebu¤ (1990) “The Devolution of Declining Industries”, Quarterly Journal of Economics, 167-186. [7] Marx, L. and S.A. Matthews (1998) “Dynamic Voluntary Contributions to a Public Project”, Discussion Paper No. 99-01, University of Pennsylvania
URI:	http://wrap.warwick.ac.uk/id/eprint/1627

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