Lockwood, Ben and Thomas, Jonathan P. (1999) Gradualism and irreversibility. Working Paper. Coventry: University of Warwick. Centre for the Study of Globalisation and Regionalisation. Working papers (University of Warwick. Centre for the Study of Globalisation and Regionalisation) (No.28/).

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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 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 Faculty of Social Sciences > Centre for the Study of Globalisation and Regionalisation
Library of Congress Subject Headings (LCSH):	Noncooperative games (Mathematics), Statistical decision, Irreversible processes, Public goods
Series Name:	Working papers (University of Warwick. Centre for the Study of Globalisation and Regionalisation)
Publisher:	University of Warwick. Centre for the Study of Globalisation and Regionalisation
Place of Publication:	Coventry
Official Date:	May 1999
Number:	No.28/
Number of Pages:	43
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
URI:	http://wrap.warwick.ac.uk/id/eprint/2097

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