Efficiency and strategy-proofness in object assignment problems with multi-demand preferences

We consider the problem of allocating sets of objects to agents and collecting payments. Each agent has a preference relation over the set of pairs consisting of a set of objects and a payment. Preferences are not necessarily quasi-linear. Non-quasi-linear preferences describe environments where the wealth effect is non-negligible: the payment level changes agents' willingness to pay for swapping sets. We investigate the existence of efficient and strategy-proof rules. A preference relation is unit-demand if given a payment level, for each set of objects, the most preferred one in the set is at least as good as the set itself; it is multi-demand if given a payment level, when an agent receives an object, receiving some additional object(s) makes him better off. We show that if a domain contains enough variety of unit-demand preferences and at least one multi-demand preference relation, and if there are more agents than objects, then no rule satises efficiency, strategy-proofness, individual rationality, and no subsidy for losers on the domain.

Keywords: Strategy-proofness, efficiency, multi-demand preferences, unit-demand preferences, non-quasi-linear preferences, minimum price Walrasian rule

JEL Classication Numbers: D44, D71, D61, D82

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