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Welfare Distribution in Two-sided Random Matching Markets

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  • Itai Ashlagi
  • Mark Braverman
  • Geng Zhao

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.

Suggested Citation

  • Itai Ashlagi & Mark Braverman & Geng Zhao, 2023. "Welfare Distribution in Two-sided Random Matching Markets," Papers 2302.08599, arXiv.org.
  • Handle: RePEc:arx:papers:2302.08599
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    References listed on IDEAS

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    3. Itai Ashlagi & Yash Kanoria & Jacob D. Leshno, 2017. "Unbalanced Random Matching Markets: The Stark Effect of Competition," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 69-98.
    4. Boris Pittel, 2019. "On Likely Solutions of the Stable Matching Problem with Unequal Numbers of Men and Women," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 122-146, February.
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    6. Gunter J. Hitsch & Ali Hortaçsu & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, vol. 100(1), pages 130-163, March.
    7. Nikhil Agarwal & Paulo Somaini, 2018. "Demand Analysis Using Strategic Reports: An Application to a School Choice Mechanism," Econometrica, Econometric Society, vol. 86(2), pages 391-444, March.
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