EEG Uminho & Online
We study information design in an infinitely repeated principal-agent environment. In each period, payoffs depend on the realization of an exogenous state generated by a Markov process. At the beginning of the game, the principal commits to an information structure that produces an action recommendation as a function of state-history. Then, in each period, the agent observes the recommendation and either obeys or exists the relationship. We seek to characterize the optimal information structure for the principal. This problem is complicated because information disclosure in a period can affect the agent’s incentives to obey in the future, due to (imperfect) state persistence. In particular, the principal can be reluctant to recommend the action that is best for both principal and agent. In extreme cases, the principal finds it optimal to not disclose any information at all. This is more likely when state persistence is high, and patience is moderate. When patience is very high, a folk-theorem type argument applies. When patience is very low, the principal does not care about the future impact of the information released in the present. It is challenging to prove that a certain information structure is optimal. Our approach is based on Lagrangian (weak) duality. The basic idea is to formulate a Lagrangian adding to the objective the agent’s (infinitely many) obedience constraints with Lagrange multipliers. An advantage of this Lagrangian problem over the original problem is that there no longer exist forward-looking constraints, and hence the solution is time-consistent, admitting a Bellman-type recursive formulation. Moreover, if the candidate optimal policy is simple, then the corresponding Bellman equation can also be simple. As an illustration, we provide sufficient conditions for optimality of no disclosure. In a more structured environment, we characterize the optimal information structures as a function of parameter values, and conduct comparative statics.
(joint work with Takuro Yamashita)
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