A note on the dynamics of incentive contracts

Laffont and Tirole (Econometrica 56:1153-1175) show that when uncertainty about an agent's ability is small, the equilibrium must involve a large amount of pooling, but, whether the continuation equilibrium induced by an optimal first-period menu of contracts is partitional or not, remains unclear. They construct a non-partitional continuation equilibrium for a given first-period menu of contracts and conjecture that this continuation equilibrium need not be suboptimal for the whole game under small uncertainty. We show that, irrespective of the amount of uncertainty, this non-partitional continuation equilibrium generates a strictly smaller payoff for the principal than a different menu of contracts with a partitional continuation equilibrium. In this sense, Laffont and Tirole's menu of contracts, giving rise to a non-partitional continuation equilibrium, is not optimal.