Randomness and Fairness in Two-Sided Matching with Limited Interviews
summary
Model has N applicants and N positions, each side draws iid uniform preferences, applicants send K applications, positions interview K' and then applicant-proposing deferred acceptance runs in the large-market limit. Exact expected matching size is derived (balls-and-bins style and DA analysis). Key findings: with K=K'=1 fraction matched → 1 - 1/e ≈ 0.632; the matching size is non-monotone in K and shows a scallop-shaped optimum at integer K; egalitarian allocation of application slots maximizes matches; limiting applications can increase overall matches when interviews are scarce.
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