Coalitional strategy-proofness and fairness

This paper considers the problem of assigning a finite number of indivisible objects, like jobs, houses, positions, etc., to the same number of individuals. There is also a divisible good (money) and 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 coalitionally strategy-proof allocation rule must maximize the use of money subject to upper quantity bounds determined by the allocation rule. If available money is nonnegative, objects may be jobs and the distribution of money a wage structure. If available money is negative, the formal model may reflect a multi-object auction. In both cases fairness means equilibrium, i.e., that each individual receives a most demanded object. I would like to thank Tommy Andersson, Bo Larsson, Zaifu Yang and the participants of the seminars in Copenhagen and Lund for helpful comments on this paper. I will also thank an anonymous referee for very valuable comments. Financial support from The Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged.