[Paper Review] An Experimental Study of Decentralized Matching

Federico Echenique, Robinson-Cortés, Alejandro+1 more|arXiv (Cornell University)|Jan 19, 2024

Game Theory and Voting Systems10 references41 citations

TL;DR

The paper experimentally studies decentralized two-sided matching without transfers, showing stable outcomes are prevalent and that the median stable matching often emerges, with cardinal preference representations influencing results and participants displaying strategic dynamics to avoid blocking cycles.

ABSTRACT

We present an experimental study of decentralized two-sided matching markets with no transfers. Experimental participants are informed of everyone's preferences and can make arbitrary non-binding match offers that get finalized when a period of market inactivity has elapsed. Several insights emerge. First, stable outcomes are prevalent. Second, while centralized clearinghouses commonly aim at implementing extremal stable matchings, our decentralized markets most frequently culminate in the median stable matching. Third, preferences' cardinal representations impact the stable partners participants match with. Last, the dynamics underlying our results exhibit strategic sophistication, with agents successfully avoiding cycles of blocking pairs.

Motivation & Objective

• Test whether decentralized, fully informed, non-transfer matching converges to stability in practice.
• Characterize which stable matchings emerge under decentralized offers (extremal vs. median).
• Examine how cardinal representations of preferences affect market outcomes.
• Explore the dynamics and strategic behavior leading to stability or blocking cycles.
• Assess robustness to market size and bargaining power.

Proposed method

• 8 participants per side in main treatments; markets run with arbitrary non-binding offers and a 30-second inactivity termination rule.
• Participants observe all payoffs from a matrix and may offer while already matched; accepted offers finalize only when inactivity ends.
• Several cardinal representations used for the same ordinal preferences to study welfare and marginal loss effects.
• Three main treatments: unique stable matching, two embedded 4-by-4 markets, and five stable matchings with three stable partners; auxiliary treatments explore unilateral offers and large markets.
• Theoretical grounding in Gale-Shapley stability, DA algorithm, and median stable matching concepts.

Experimental results

Research questions

• RQ1 Do decentralized interactions produce stable matchings in practice under complete information and no transfers?
• RQ2 Which stable matchings (extremal vs. median) are more likely to be realized in decentralized settings?
• RQ3 How do cardinal representations of preferences influence the selected stable matching?
• RQ4 What do the dynamics (offers, rejections, cycles) look like, and do participants avoid blocking cycles?
• RQ5 Are results robust to larger markets or restricted bargaining power?

Key findings

• Stable outcomes are prevalent; 88% of markets reach a stable matching.
• Most markets converge quickly with an average of 46 offers and under two minutes of market time.
• Median stable matching is the modal outcome; 77% of pairings are with median stable partners, and 80% of markets converge to the market-wide median stable matching.
• Cardinal representation of preferences significantly influences the stable matching selected; e.g., higher cardinal incentives to colors or foods bias toward the color- or food-optimal stable matching.
• Markets with three stable partners see higher incidence of median partner matches, yet stability remains common even when one side cannot make offers (unilateral treatment).
• Dynamics show strategic sophistication: agents target blocking partners more when they gain more from the match, and not all blocking offers are accepted, helping avoid cycles.
• Simulations of existing dynamic models do not fit the data well; strategies incorporating history and strategic offer-making better explain observed outcomes.