Perfect Robust Implementation by Private Information Design

This paper studies the principal-agent framework in which the principal wants to implement his first-best action. The principal privately selects a signal structure about the unknown state of the agent whose preferences depend on the principal's action, the state and a privately known agent's type. The agent privately observes the generated signal and reports it to the principal. 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. The key idea is that a randomization between signal structures forms posterior beliefs, which induce actions with opposite reactions to agent's messages. As to the economic application, we consider the bilateral-trade model and show that the seller can extract the full surplus from the privately informed buyer with non-quasilinear preferences and multi-dimensional information