Serial dictatorship mechanisms with reservation prices

Abstract

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 ϕ satisfies minimal tradability, individual rationality, strategy-proofness, consistency, and non wasteful tie-breaking if and only if there exists a reservation price vector r and a priority ordering such that ϕ is a serial dictatorship mechanism with reservation prices based on r and . We obtain a second characterization by replacing individual rationality with non-imposition. In both our characterizations r, , and ϕ 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.JEL classification: C78, D47, D71

Serial dictatorship mechanisms with reservation prices: heterogeneous objects

“…Minimal tradability was first introduced for single-object problems by Sakai (2013), and then extended to problems with homogeneous objects by Klaus and Nichifor (2020). Our definition of minimal tradability coincides with that of Sakai's (2013) for single-object problems, but it is in character less demanding than that of Klaus and Nichifor (2020).…”

“…Our model extends the homogeneous objects model of Klaus and Nichifor (2020) to heterogeneous objects; to ease the comparison, our exposition and notation are closely based on that of Klaus and Nichifor (2020).…”

“…Independence of unallocated objects was introduced for a homogeneous objects allocation model by Klaus and Nichifor (2020) who required that removing all unallocated objects leaves an outcome unchanged. We extend their property to allow for heterogeneous objects, and we require that only some, but not necessary all, unallocated objects be removed.…”

“…Our last property requires that a mechanism does not select an outcome where an agent is indifferent between [receiving a real object at some price] and [not receiving an object and not paying anything, i.e., withdrawing from the market]. Klaus and Nichifor (2020), is a mild efficiency requirement: The tie-breaking, which rules out allocating a real object at some price to an agent who is indifferent between such an allotment and withdrawing from the market, is non-wasteful in that it keeps the object available, because another agent might strictly prefer to receive it.…”

“…Our work is closely related to that of Klaus and Nichifor (2020). We extend their homogeneous indivisible objects model, normative properties, and the class of serial dictatorship mechanisms with reservation prices that they introduced, to heterogeneous indivisible objects.…”