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Approximating Gains-from-Trade in Matching Markets

Moshe Babaioff, Aviad Rubinstein, Xizhi Tan, Kangning Wang

Abstract

A central challenge in mechanism design is to develop truthful trade mechanisms that maximize the expected gains-from-trade (GFT) in two-sided markets with strategic agents. As achieving the full GFT is generally impossible, much of the literature has focused on constant-factor approximations. Existing results, however, are limited to the highly structured settings of bilateral trade and double auctions, in which every buyer can trade with every seller. We consider the significantly more general setting of two-sided matching markets with arbitrary downward-closed constraints on the family of allowed matchings. For this setting, we present a simple randomized truthful mechanism that guarantees a constant-factor approximation to the optimal expected GFT. This result also resolves an open problem posed by Cai, Goldner, Ma, and Zhao (2021).

Approximating Gains-from-Trade in Matching Markets

Abstract

A central challenge in mechanism design is to develop truthful trade mechanisms that maximize the expected gains-from-trade (GFT) in two-sided markets with strategic agents. As achieving the full GFT is generally impossible, much of the literature has focused on constant-factor approximations. Existing results, however, are limited to the highly structured settings of bilateral trade and double auctions, in which every buyer can trade with every seller. We consider the significantly more general setting of two-sided matching markets with arbitrary downward-closed constraints on the family of allowed matchings. For this setting, we present a simple randomized truthful mechanism that guarantees a constant-factor approximation to the optimal expected GFT. This result also resolves an open problem posed by Cai, Goldner, Ma, and Zhao (2021).

Paper Structure

This paper contains 34 sections, 28 theorems, 67 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Gains-from-trade in matching markets.
  3. Our Results
  4. Technical Overview
  5. Preliminaries: constant factor in a single-edge graph dmsw22.
  6. Candidate graph 1: the ex-post GFT graph.
  7. Candidate graph 2: the ex-ante expected GFT graph.
  8. Candidate graphs 3,4,$\ldots$
  9. Our Analysis Approach: Regrouping and the Meta-Auction.
  10. Related Work
  11. Gains-from-trade approximation.
  12. Welfare approximation in bilateral trade.
  13. Two-sided markets.
  14. Preliminaries
  15. Matching market.
  16. ...and 19 more sections

Key Result

Theorem 1.1

Consider any Bayesian single-dimensional matching market with independent distributions that is constrained by a downward-closed family of feasible matchings. The mechanism that randomizes between GSOM and GBOM with equal probability satisfies dominant-strategy incentive-compatibility (DSIC), ex-pos

Theorems & Definitions (57)

  • Theorem 1.1
  • Remark 1.2
  • Remark 1.3
  • Corollary : Informal
  • Theorem 2.1: Implementability and Payment Formula Myerson81
  • Definition 2.2: Threshold Payments
  • Theorem 2.3: BCWZ17
  • Theorem 2.4
  • Theorem \ref{thm:main_result_BIC_DSIC_formal}
  • Corollary \ref{thm:main_result_BIC_DSIC_formal}
  • ...and 47 more