We study the distribution of envy in random matching markets under the Deferred Acceptance (DA) algorithm. Using tools from applied probability, we compute the expected number of proposing agents whom nobody envies and those who envy nobody. We obtain an exact finite-market expression for the former, based on a connection with the coupon collector problem, and asymptotic bounds for the latter. To put these quantities into perspective, we compare them to their counterparts under Random Serial Dictatorship (RSD): while RSD assigns a constant fraction of agents to their top choice, both DA and RSD leave exactly H n proposing agents unenvied in expectation. Our results show that these clearly unimprovable proposing agents constitute a vanishing fraction of the market. • We study the distribution of envy in random matching markets. • We derive exact expressions under Deferred Acceptance. • The expected number of unenvied students equals the n th harmonic number. • Students receiving top choices follow an approximately geometric rank distribution. • DA and Random Serial Dictatorship produce identical numbers of unenvied students. • Both unenvied and envy-free student fractions vanish asymptotically.
Ortega et al. (Wed,) studied this question.