Perfect robust implementation by private information design

This paper studies the general principal-agent framework in which the principal aims to implement his first-best action that is monotone in the unknown state. The principal privately selects a signal structure of the agent whose payoff depends on the principal’s action, the state, and the privately known type. The agent privately observes the generated signal and reports it to the principal, who takes action. We show that by randomizing between two perfectly informative signal structures, the principal can elicit perfect information from the agent about the state and implement his first-best action regardless of the agent’s type. As to the economic application, we consider the bilateral trade model with non-quasilinear preferences and private multi-dimensional information of the buyer, and show that the seller can extract full surplus by privately designing the buyer’s signal structures.