Conferences at Department of Economics, University of Toronto, Canadian Economic Theory Conference 2022

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Perfect Robust Implementation by Private Information Design

Maxim Ivanov*

Last modified: 2022-04-17


This paper studies the principal-agent framework in which the principal (e.g., the decision-maker or the seller) wants to implement his first-best action that is monotone in the unknown state. The principal privately selects a signal structure about the state of the agent (e.g., the sender or the buyer) whose preferences depend on the action and potentially on the state as well as on a privately known agent's type. The agent privately observes the signal generated by the signal structure and sends a message 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 the first-best action regardless of the agent's type. We provide the precise characterization of such signal structures. The key idea is that signal structures form posterior beliefs, which induce actions that react oppositely to agent's messages. This sustains agent's truthtelling and allows the principal to perfectly learn the state and implement his first-best decision. 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.

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