This paper considers a class of two-player dynamic games in which each player controls a one-dimensional action variable, interpreted as a level of cooperation. The dynamics are due to an irreversibility constraint: neither player can ever reduce his cooperation level. Payoffs are decreasing in one's own action, increasing in one's opponent's action. We characterize efficient symmetric equilibrium action paths; actions rise gradually over time and converge, when payoffs are smooth, to a level strictly below the one-shot efficient level, no matter how little discounting takes place. The analysis is extended to incorporate sequential moves and asymmetric equilibria. Copyright 2002, Wiley-Blackwell.

Recent work on consumption allocations in village economies finds that idiosyncratic variation in consumption is systematically related to idiosyncratic variation in income, thus rejecting the hypothesis of full risk-pooling. We attempt to explain these observations by adding limited commitment as an impediment to risk-pooling. We provide a general dynamic model and completely characterise efficient informal insurance arrangements constrained by limited commitment, and test the model using data from three Indian villages. We find that the model can fully explain the dynamic response of consumption to income, but that it fails to explain the distribution of consumption across households.