Multilateral Matching Under Dichotomous Preferences

For any multilateral matching problem with dichotomous preferences, in the sense that agents are indifferent between all acceptable teams, there exist some strategy proof, individually rational and efficient mechanisms. Moreover some random matching mechanisms simultaneously satisfy the three crucial desiderata of mechanism design: efficiency, fairness and strategyproofness, which typically conflict even in simple matching problems. The results hold for a novel criterion of fairness. I prove a non-existence result for the weakest fairness criterion that is standardly used: no ex-post Pareto optimal and individually rational mechanism for multilateral matching problem treats