Gradualism and Irreversibility
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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