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 …

mild fairness notion called local envy-freeness, some new theoretical support is provided for this widely used rule in … practice. Among strategy-proof, symmetric and locally envy-free rules, there exists an ex-post constrained efficient (ex … strategy-proof, ex-post stable and locally envy-free rules, there exists one that is symmetric at the top if and only if DA …

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