Serial Dictatorship Mechanisms with Reservation Prices

We propose a new set of mechanisms, which we call serial dictatorship mechanisms with reservation prices for the allocation of one indivisible good. We show that a mechanism satisfies minimal tradability, individual rationality, strategy-proofness, consistency, and non wasteful tie-breaking if and only if there exists a reservation price vector and a priority ordering such that the mechanism is a serial dictatorship mechanism with reservation prices. We obtain a second characterization by replacing individual rationality with non-imposition. In both our characterizations the reservation price vector, the priority ordering, and the mechanism are all found simultaneously and endogenously from the properties. In addition, we show that in our model a mechanism satisfies Pareto efficiency, strategy-proofness, and consistency if and only if it is welfare equivalent to a classical serial dictatorship. Finally, we illustrate how the normative requirements governing the functioning of some real life markets and the mechanisms that these markets use are reasonably well captured by our model and results.