(Regular readers of this blog will know I consider that a good thing.)

Market mechanisms of all sorts are plagued in practice by the problem of unraveling.  For example, well before completing law school, law students sign contracts to assume positions at established law firms.  Unraveling occurs when this early contracting motive causes market participants to compete by exiting the market earlier and earlier to the detriment of market efficiency.  An excellent summary of the problem and a slew of examples can be found in a paper by Roth and Xing.

One of the problems is that the formal market institutions were not designed to combat unraveling.  The adoption of stable matching mechanisms is often proposed as a solution.  A famous example is the National Medical Resident Matching program which matches residents to hospitals, a stable matching mechanism that is widely believed to have significantly curtailed unraveling in that market.

Nevertheless unraveling is a robust phenomenon and Songzi Du, in a joint paper with Yair Livne, from Stanford GSB has a very simple theoretical explanation.  Indeed, he shows that unraveling incentives are strong even in markets with a stable matching mechanism.  Moreover large market size seems only to make the problem worse.

Consider an employer and employee who are both highly ranked and suppose that they meet each other well before the matching process begins so that neither has learned anything about the quality of the rest of the market.  Let’s analyze their incentives to sign a contract now and exit the market before the formal matching process takes place.

The employee reasons that the mechanism is either going to give him a better match or its going to give the employer a better match. If he, the employee, gets a better match it is not likely to be that much better since the current employer is already highly ranked.  On the other hand, if the employer finds a better match then the employee is going to have to take his chances with the rest of the market.  Since the current employer is highly ranked, it is likely that whatever new employer he is matched with will be significantly worse.

On average going to the matching mechanism is a bad gamble.  And since the employer is in the exact same situation, they both prefer to exit than to take that gamble.

Du and Livne use this idea to quantify how large a problem unraveling is likely to be.  They takes the realistic position that participants are going to learn about the quality of close competitors prior to contracting. This gives them a rough sense of the possible matches they will get from the mechanism.  The previous intution translates naturally to this setting.  If the two potential early contractors are near the high end of this group, they will want to match early.  Du and Livne show that for any given similarly ranked pair, this will happen about 1/4 of the time, and this is true even when the market is very large.

Finally, once it is established that unraveling is the norm and not the exception, he uses a dynamic model to give a sense of what kind of equilibrium an unraveled market settles into.  And the news here is not good either.  No matter how you try to make the match work, by assigning some to match early and some to wait, there will always be some pairs that want to deviate from that plan.  That is, there is no equilibrium.

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