When Matching Market Participants Imperfectly Learn, Who Ends Up Matched With Whom?

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Laure Goursat (master APE)

According to Nobel Prize winner Alvin Roth (1), a matching market is “a market in which prices do not do all the work”. Examples of such markets include college admissions, organ donation (matching without transfers - forbidding monetary exchanges), or labor market, even marriage (matching with transfers - allowing monetary exchanges). In particular on such markets, prices do not do the usual simplifying work they usually perform on classical markets, that is they do not aggregate supply and demand parameters into one single indicator relevant for individual decisions. Matching market participants are therefore left to play with multi-dimensional parameters causing feedback data and competition scheme to be highly complex. The issue is that this multi-dimensional complexity far exceeds the obvious and documented mind limitations of human beings. As a consequence, matching market participants are doomed to act with bounded rationality (namely, they are unable to always choose the right strategy so as to maximise their objectives).

In this article, Laure Goursat provides a tentative answer to the following: First, what is the nature of bounded rationality on matching markets? And second, does it reshuffle the matching outcome and if so, in what direction? This amounts to making a novel yet meaningful connection between economics of matching and behavior, through a tailor-made concept of bounded rationality for matching markets. The underlying ambition is to shed lights on a variety of empirical puzzles on matching markets that are left unexplained under the full rationality premise.

In this perspective, she proposes a simple cognitive procedure that matching market participants may follow on an imperfect information matching market, where a participant only observes the surpluses of the realised matches. To estimate the surplus from a potential unrealised match between him and a targeted partner, a so-called Live-Polarised-Unidimensional-Valuation (LPUV) rational agent extrapolates from the observed surplus generated by the targeted partner and the targeted partner’s current match. Stated for the marriage market for instance, it means that a LPUV-rational man m looks at outward signs of happiness from a woman w’s current marriage to assess whether he m would be happy by marrying w. The estimates of match utilities are thus endogenous to the current market situation and in general they do not fit the true utilities.

The issue is that the mistake made at the individual level disrupts the allocation formed at the collective level. More specifically, considering that stable matchings are the ones that are bound to arise and maintain over time, Laure GOURSAT focuses on implications of LPUV-rationality for stable allocations. As a reminder, a matching is said to be stable if no currently matched agent would prefer to stay unmatched, and no pair of two agents that are not currently matched together would prefer to be so. When agents are fully rational, this defines the usual [referred to as Gale-Shapley, GS (2)] stability notion. When agents are boundedly rational in a LPUV fashion, this defines a new LPUV-stability concept. Comparing both, she finds three interesting predictions. First, LPUV-stable (resp. GS-stable) matchings are biased towards matchings where few (resp. numerous) individuals are matched. Second, in some cases a reasonably fair splitting between partners can make a matching LPUV-stable whatever the surpluses, whereas there is no such splitting that would guarantee GS-stability regardless of the surpluses. Third, when the splitting rule is defined (using marriage vocabulary again) to be a ratio between spouses’ exogenous bargaining scores, the positive assortative matching (the one that matches the strongest men to the strongest women and conversely) is more often LPUV-stable than GS-stable. This stands as preliminary evidence that the proposed LPUV-stability concept can account for the long-established empirical puzzle on assortativity on matching markets.

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References
(1) Social Science Bites (podcast), published on August 1, 2017
(2) D. Gale and L. S. Shapley. “College Admissions and the Stability of Marriage”. In : The American Mathematical Monthly 69.1 (1962), pp. 9–15

Master’s thesis title : “Imperfect Social Learning on Matching Markets : Implications for Stability”
Under the direction of : Philippe Jehiel
Available at : https://dumas.ccsd.cnrs.fr/dumas-02407515

Photo credit : Freedom my wing (Shutterstock)