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

Consider the problem of allocating objects to agents and how much they should pay. Each agent has a preference relation over pairs of a set of objects and a payment. Preferences are not necessarily quasi-linear. Non-quasi-linear preferences describe environments where payments influence agents’ abilities to utilize objects. This paper is to investigate the possibility of designing efficient and strategy-proof rules in such environments. A preference relation is single demand if an agent wishes to receive at most one object; it is multi demand if whenever an agent receives one object, an additional object makes him better off. We show that if a domain contains all the single demand preferences and at least one multi demand preference relation, and there are more agents than objects, then no rule satisfies efficiency, strategy-proofness, individual rationality, and no subsidy for losers on the domain.