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Self-Confirming Mechanisms

Zhiming Feng, Qingmin Liu

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.

Self-Confirming Mechanisms

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.
Paper Structure (25 sections, 14 theorems, 113 equations)

This paper contains 25 sections, 14 theorems, 113 equations.

Table of Contents

  1. Introduction
  2. Basics
  3. Mathematical Notation
  4. Mechanism-Induced Game
  5. Mechanism-Generated Data and Inference
  6. Fictitious Revelation Principle
  7. Direct Mechanisms
  8. Fictitious Direct Mechanisms
  9. Fictitious Revelation Principle
  10. Strong Form
  11. Weak Form
  12. Self-Confirming Mechanisms
  13. Definition
  14. Grain-of-Truth Refinement
  15. Application: Monopoly
  16. ...and 10 more sections

Key Result

Theorem 1

Every fictitious direct mechanism $(\mathcal{D}, \varphi)$ admits an equivalent augmented mechanism $(\mathcal{M}, \sigma)$. Conversely, if for each $i\in N$ the type space $\Theta^i$ and the message space $M^i$ are uncountable standard Borel spaces, then every augmented mechanism $(\mathcal{M}, \si

Theorems & Definitions (44)

  • Remark 1
  • Remark 2: Topology and Measurability
  • Definition 1
  • Remark 3
  • Example 1
  • Example 2
  • Definition 2
  • Remark 4
  • Definition 3
  • Remark 5
  • ...and 34 more