Local incentive compatibility with transfers

We consider locally incentive compatible mechanisms with deterministic allocation rules and transfers with quasilinear utility. We identify a rich class of type spaces, which includes the single peaked type space, where local incentive compatibility does not imply incentive compatibility. Our main result shows that in such type spaces, a mechanism is locally incentive compatible and payment-only incentive compatible if and only if it is incentive compatible. Payment-only incentive compatibility requires that a mechanism that generates the same allocation at two types must have the same payment at those two types. Our result works on a class of ordinal type spaces, which are generated by considering a set of ordinal preferences over alternatives and then considering all non-negative type vectors representing such preferences.