Fairness and efficiency in strategy-proof object allocation mechanisms

I consider the problem of allocating N indivisible objects among N agents according to their preferences when transfers are absent and an outside option may exist. I study the tradeo between fairness and e ciency in the class of strategy-proof mechanisms. The main nding is that for strategy-proof mechanisms the following e ciency and fairness criteria are mutually incompatible: (1) ex-post e ciency and envy-freeness, (2) ordinal e ciency and weak envy-freeness, and (3) ordinal e ciency and equal division lower bound. Result 1 is the rst impossibility result for this setting that uses ex-post e ciency; results 2 and 3 are more practical than similar results in the literature. In addition, for N = 3, I provide two characterizations of the celebrated random serial dictatorship mechanism: it is the unique strategy-proof, ex-post e cient mechanism that (4) provides agents that have the same ordinal preferences with assignments not dominated by each other (weak envy-freeness among equals), or (5) provides agents that have the same cardinal preferences with assignments of equal expected utility (symmetry). These results strengthen the characterization by Bogomolnaia and Moulin (2001); result 5 implies the impossibility result by Zhou (1990). JEL Classi cation: C78; D71; D78