Preference Manipulations Lead to the Uniform Rule

Abstract

In the division problem with single-peaked preferences, it is well known that the uniform rule is robust to strategic manipulation. Furthermore, under e¢ ciency and symmetry, it is the unique strategy-proof rule (Sprumont, 1991; Ching, 1994). We conversely analyze the consequences of strategic manipulation for a wide class of rules. Given a rule, we interpret its associated direct revelation game as a manipulation game, and we characterize its equilibrium allocations. We establish a strong connection between outcomes of manipulation and the uniform rule itself. For every rule that belongs to the class, the uniform allocation (i) is the unique strong Nash equilibrium allocation and the unique Pareto-e¢ cient Nash equilibrium allocation, and (ii) is the unique Nash equilibrium allocation under an additional strict monotonicity condition. Thus, attempts to manipulate each of our rule lead to the recommendation made by the uniform rule. A by-product of our results is the identi…cation of a large class of direct revelation mechanisms that doubly implement the uniform rule in Nash and strong Nash equilibria.