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Welfare effects of limiting the number of interviews by Beyhaghi and Tardos

Here's a new paper on a subject that is coming up in a number of the markets that I keep an eye on:

Effect of Limited Number of Interviews onMatching Markets
by Hedyeh Beyhaghi and Eva Tardos

Abstract. We study outcome of two-sided matching between prospective medical residents who can only apply to a limited number of positions and hospitals who can interview only a limited number of applicants and show non-intuitive effects in the matching outcomes. We study matching size as our notion of efficiency, and show when the number of interviews is limited, a market with limited number of applications achieves a higher efficiency compared to a market with no limit. Also we find that a system of treating all applicants equally (setting the same limit for their number of applications), is more efficient rather than allowing a small set to apply to one more/less position. This comparison results in a scallop-shape figure 2 that shows expected size of matching with respect to expected number of applications. Finally we show that limiting number of interviews does not always hurt efficiency of matching markets and can improve social welfare in certain cases. 

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