DYNAMIC CONTRACT WITH UNCERTAINTY

Abstract

This paper studies the optimal contract design with moral hazard issue and incomplete information on the agent side. The agent updates his belief contingent on the outcome in the round in which he has exerted effort while the principal can only make a reference on the agent?s belief based on outcome at each round and the agent?s initial belief. We have considered three scenarios: two stage model, infinite stage model with extremal states and infinite stage model without extremal states. In the first scenario, we have found the equivalence among front-loading bonus, back-loading bonus and superior state wage where the back-loading bonus and superior state wage are used to create cross-state incentive to balance not only the cost but also the belief-discrepancy gain. In the second scenario, we have proved the strict dominance of bonus over wage regardless of initial belief, discount factor and the constant ? due to the assumption of Bayesian Belief Updating Rule. We have also proved that at optimum, the IC constraints hold due to the zig-zag property, which excludes excessive front-loading, plus with the time-persistent effect of belief distortion, which avoids excessive back-loading. In the last scenario, I have derived the functional form of the minimum cost function and have given a way to solve this problem explicitly by using dynamic system theory.