which a woman proposes to a random man in each step. We prove that envy in a matching market is bounded by envy in this … class of mechanisms, in which there is just one woman and two types of men. We conclude that envy is bounded by the inverse … of the square root of the number of men in each type. Therefore, in large matching markets, envy becomes zero; on top of …

In priority-based matching problems, there is a trade-off between efficiency andreducing justified-envy. We show that … finding an efficient and justified-envy minimalmatching is an NP-hard problem when objects have weak priority rankings … and strategyproof mechanisms and show thatno group-strategyproof mechanism minimizes justified-envy in that class. Then …

's complementary subset, given that such an envy-free division is possible. We show that the possibility of one player's undercutting … generally leads to an envy-free division, even when the players rank items exactly the same. Although the undercut procedure is …

. To study centralized college admissions, I advance the theory of stability for many-to-many matching markets with …

random allocations from deterministic allocation mechanisms. Insights from the two-sided matching theory and the recent …