Efficiency and strategy-proofness in object allocation problems with payments: Externalities with income effects

We consider the problem of allocating an object to n ≥ 2 agents with payments. We allow agents to have preferences that exhibit (allocative) externalities and are not necessarily quasi-linear. Thus, agents care not only their own consumption of the object but also other agents’ consumption or the owner keeping the object. A preference of an agent is identity-independent if he does not care who else (except for the owner) wins the object at the payment of zero. We show that if (i) all the agents have identity-independent preferences, and (ii) at least n − 1 agents have preferences that exhibit positive externalities, then the generalized pivotal rule is the only rule satisfying efficiency, weak individual rationality, no subsidy for losers, and strategy-proofness. We also establish that if we relax one of the assumptions (i) and (ii), then no rule satisfies the four properties. Further, we find the two environments where some agents may have identity-dependent preferences, others have quasi-linear preferences exhibiting positive externaliteis, and there is a rule satisfying the four properties. Overall, our results suggest the importance of identity-independence and positive externalities in a non-quasi-linear environment with externalities for the existence of a rule satisfying the four properties.