Non-obvious manipulability and efficiency in package assignment problems with money for agents with income effects and hard budget constraints

Abstract:

We study a problem of assigning packages of objects to agents with money. We allow agents to have utility functions that exhibit income effects or face hard budget constraints. It is already known that one of income effects and hard budget con-straints lead to the non-existence of a rule satisfying strategy-proofness, efficiency, individual rationality, and no subsidy (Dobzinski et al., 2012; Kazumura and Serizawa, 2016; Baisa; 2020, Malik and Mishra, 2021, etc.). Given such negative results, we search for rules satisfying non-obvious manipulability (Troyan and Morrill, 2020), an incentive property weaker than strategy-proofness, together with the other three properties. First, we identify a necessary and sufficient condition for a rule satisfying efficiency, individual rationality, and no subsidy to be non-obviously manipulable. By using the first result, we show that a slight modification of a (truncated) pay as bid rule satisfies non-obvious manipulability, efficiency, individual rationality, and no subsidy.