We consider the problem of designing a mechanism to allocate objects to agents when each agent has a quota that must be filled exactly. Agents are assumed to have responsive preferences over items. We show that the only strategy-proof, Pareto optimal, and nonbossy mechanisms are sequential dictatorships. We also show that the only strategy-proof, Pareto optimal, nonbossy, and neutral mechanisms are serial dictatorships. Since these negative results hold for responsive preferences, they hold for more general preferences as well.
Ehlers L, Klaus B (2003) Coalitional strategy-proof and resource monotonic solutions for multiple assignment problems. Soc Choice Welfare 21: 265–280CrossRefGoogle Scholar
Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41: 587–601CrossRefGoogle Scholar
Jackson MO (2003) Mechanism theory. In: Ulrich D (ed) Optimization and operations research, in Encyclopedia of Life Support Systems. EOLSS Publishers, Oxford, http://eolss.net
Papai S (2001) Strategy-proof and nonbossy multiple assignments. J Public Econ Theory 3: 257–271CrossRefGoogle Scholar
Satterthwaite MA (1975) Strategy proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10: 187–216CrossRefGoogle Scholar
Satterthwaite MA, Sonnenschein H (1981) Strategy-proof at differentiable points. Rev Econ Stud 48: 587–597CrossRefGoogle Scholar