Self-Confirming Mechanisms

TL;DR

This paper introduces the concept of self-confirming mechanisms in environments where the mechanism designer learns about agents' private information through their behavior, and characterizes optimal mechanisms under this framework.

Contribution

It formalizes self-confirming mechanisms, proves a fictitious revelation principle, and characterizes dominant-strategy self-confirming mechanisms as posted-price mechanisms in a monopoly setting.

Findings

Self-confirming mechanisms align incentives with the information produced by agents.

A fictitious revelation principle allows representation of incentive-compatible mechanisms as filtered type reports.

In monopoly problems, self-confirming mechanisms are equivalent to posted-price mechanisms with revenue-maximizing prices.

Abstract

This paper studies mechanism design environments in which the designer does not know the distribution of agents' private information a priori and instead learns from agents' behavior induced by the mechanism itself. We formalize a notion of self-confirming mechanisms and a refinement thereof, capturing the idea that an equilibrium mechanism is optimal given the designer's belief and that this belief is consistent with the information produced by the mechanism. We establish a fictitious revelation principle, showing that any incentive-compatible mechanism can be represented as a direct mechanism with filtered type reports that preserve the original mechanism's informational content. Applying the framework to a monopoly problem, we show that, subject to an equilibrium refinement, dominant-strategy self-confirming mechanisms are exactly posted-price mechanisms with locally revenue-maximizing prices.