Robust group strategy-proof rules in the object allocation problem with money: The role of tie-breaking rules

We study the object allocation problem with money. The owner owns identical objects. Each agent receives at most one unit of the object, and has a preference that is not necessarily quasi-linear. Recently, Kivinen and Tumennasan (2021) propose a group incentive property that they call robust group strategy-proofness. It takes into account a coalitional manipulation with which a coalition agrees without knowing the other agents’ preferences. We propose a generalized Vickrey rule with lowest priority agents that is associated with a tie-breaking rule such that for each coalitional report of preferences, there is an agent (a lowest priority agent) who has a chance to receive the object only after all the other members of the coalition receive the object. We show that the generalized Vickrey rules with lowest priority agents are the only rules satisfying robust group strategy-proofness, efficiency, individual rationality, and no subsidy for losers. Our result highlights the importance of the tie-breaking rules for robust group strategy-proofness, which contrasts with group strategy-proofness that a generalized Vickrey rule satisfies regardless of the tie-breaking rule.