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Calibrated Mechanism Design

Laura Doval, Alex Smolin

Abstract

We study mechanism design when a designer repeatedly uses a fixed mechanism to interact with strategic agents who learn from observing their allocations. We introduce a static framework, calibrated mechanism design, requiring mechanisms to remain incentive compatible given the information they reveal about an underlying state through repeated use. In single-agent settings, we prove implementable outcomes correspond to two-stage mechanisms: the designer discloses information about the state, then commits to a state-independent allocation rule. This yields a tractable procedure to characterize calibrated mechanisms, combining information design and mechanism design. In private values environments, full transparency is optimal and correlation-based surplus extraction fails. We provide a microfoundation by showing calibrated mechanisms characterize exactly what is implementable when an infinitely patient agent repeatedly interacts with the same mechanism. Dynamic mechanisms that condition on histories expand implementable outcomes only by weakening incentive constraints, but not by enriching the designer's ability to obfuscate learning.

Calibrated Mechanism Design

Abstract

We study mechanism design when a designer repeatedly uses a fixed mechanism to interact with strategic agents who learn from observing their allocations. We introduce a static framework, calibrated mechanism design, requiring mechanisms to remain incentive compatible given the information they reveal about an underlying state through repeated use. In single-agent settings, we prove implementable outcomes correspond to two-stage mechanisms: the designer discloses information about the state, then commits to a state-independent allocation rule. This yields a tractable procedure to characterize calibrated mechanisms, combining information design and mechanism design. In private values environments, full transparency is optimal and correlation-based surplus extraction fails. We provide a microfoundation by showing calibrated mechanisms characterize exactly what is implementable when an infinitely patient agent repeatedly interacts with the same mechanism. Dynamic mechanisms that condition on histories expand implementable outcomes only by weakening incentive constraints, but not by enriching the designer's ability to obfuscate learning.

Paper Structure

This paper contains 78 sections, 17 theorems, 209 equations, 2 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Calibrated Mechanism Design
  4. Primitives
  5. Mechanisms
  6. Calibrated information structures
  7. Information leakage from a mechanism
  8. Calibrated Mechanism Design
  9. Private value environments
  10. Two-stage mechanisms
  11. Single-agent case and two-stage mechanisms
  12. Two-stage mechanisms solve calibrated mechanism design
  13. Multiple agents and generalized two-stage mechanisms
  14. Applications
  15. Calibrated Screening
  16. ...and 63 more sections

Key Result

Theorem 2.1

Under private values, the designer's payoff under the optimal calibrated mechanism is the same payoff he would obtain by choosing $\phi_\text{full}$.

Figures (2)

  • Figure 3.1: Seller's payoff in \ref{['example:cml']}.
  • Figure 3.2: Seller's profit in the two-stage mechanism

Theorems & Definitions (42)

  • Definition 1: Calibrated information structures
  • Definition 2: Calibrated Mechanism Design
  • Example 1: Selling a good under demand uncertainty
  • Theorem 2.1: Private values
  • Definition 3: Two-stage mechanisms
  • Theorem 3.1: Two-stage and calibrated mechanisms
  • Example 1: continued
  • Example 2: Horizontal differentiation
  • Corollary 3.1: Support of calibrated information structures
  • Definition 4: Generalized two-stage mechanism
  • ...and 32 more