Coalition Strategy-Proofness and Fairness

This paper considers a fair division problem with indivisible objects, like jobs, houses, positions, etc., and one divisible good (money). The individuals consume money and one object each. The class of fair allocation rules that are strategy-proof in the strong sense that no coalition of individuals can improve the allocation for all of its members, by misrepresenting their preferences, is characterized. It turns out that given a regularity condition, the outcome of a fair and coalition strategy-proof allocation rule must maximize the use of money subject to upper quantity bounds determined by the allocation rule. Due to these restrictions the outcomes of the allocation rule are Pareto efficient only for some preference profiles. In a multi-object auction interpretation of the model, the result is a complete characterization of coalition strategy-proof auction rules.