Welfare Distribution in Two-sided Random Matching Markets

TL;DR

This paper analyzes welfare distribution in large two-sided random matching markets, revealing how intrinsic fitness and global parameters shape stable outcomes and agent welfare distributions.

Contribution

It introduces the concept of intrinsic fitness to characterize agent competitiveness and provides a tight description of stable outcomes under a logit preference model.

Findings

Stable outcomes are characterized by intrinsic fitness values.

Agent welfare scaled by fitness follows an exponential distribution.

Average welfare on one side determines the other side's average welfare.

Abstract

We study the welfare structure in two-sided large random matching markets. In the model, each agent has a latent personal score for every agent on the other side of the market and her preferences follow a logit model based on these scores. Under a contiguity condition, we provide a tight description of stable outcomes. First, we identify an intrinsic fitness for each agent that represents her relative competitiveness in the market, independent of the realized stable outcome. The intrinsic fitness values correspond to scaling coefficients needed to make a latent mutual matrix bi-stochastic, where the latent scores can be interpreted as a-priori probabilities of a pair being matched. Second, in every stable (or even approximately stable) matching, the welfare or the ranks of the agents on each side of the market, when scaled by their intrinsic fitness, have an approximately exponential empirical distribution. Moreover, the average welfare of agents on one side of the market is sufficient to determine the average on the other side. Overall, each agent's welfare is determined by a global parameter, her intrinsic fitness, and an extrinsic factor with exponential distribution across the population.