Approximate efficiency and strategy-proofness for moneyless mechanisms on single-dipped policy domain

The single-dipped domain can be used to model any allocation problem where a single output must be chosen in an interval with the assumption that agents' preferences have a single most loathful point (the dip) in the interval, and the preferences are increasing as one moves away from that dip. Practical domains like this appear in political voting system where each voter has his most-hated candidate and alternative candidates are evaluated by their proximity to this candidate or in obnoxious location problem, where each agent prefers to have the obnoxious location to be distant from his own location, among others. We first characterize deterministic and anonymous strategy-proof and group strategy-proof mechanisms on single-dipped public policy domain, complementing the well-known results on single-peaked policy domain first investigated by Moulin (Pub. Choice 35:437-455, 1980). Then we consider the tradeoff between strategy-proofness and efficiency by applying our characterization. As concrete applications of our results, we extend existing models and results, and resolve several open questions related to the obnoxious facility location game from the algorithmic mechanism design literature.