Characterizing Pairwise Strategy-proof Rules in Object Allocation Problems with Money

We consider the problem of allocating a single object to the agents with payments. Agents have preferences that are not necessarily quasi-linear. We characterize the class of rules satisfying pairwise strategy-proofness and non-imposition by the priority rule. Our characterization result remains valid even if we replace pairwise strategy-proofness by either weaker effectively pairwise strategy-proofness or stronger group strategy-proofness. By exploiting our characterization, we identify the class of rules satisfying both the properties that are in addition (i) onto, (ii) welfare continuous, (iii) minimally fair , (iv) constrained efficient within the class of rules satisfying both the properties, or (v) revenue undominated within the class of rules satisfying the properties, and find the tension between minimal properties of efficiency, fairness, and revenue maximization under pairwise strategy-proofness