Efficient Multi-Unit Auctions for Normal Goods

Abstract

I study multiunit auction design when bidders have private values, multiunit demands, and non‐quasilinear preferences. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. I give conditions under which we can design a mechanism that retains the Vickrey auction's desirable incentive and efficiency properties: (1) individual rationality, (2) dominant strategy incentive compatibility, and (3) Pareto efficiency. I show that there is a mechanism that retains the desired properties of the Vickrey auction if there are two bidders who have single‐dimensional types. I also present an impossibility theorem that shows that there is no mechanism that satisfies Vickrey's desired properties and weak budget balance when bidders have multidimensional types.

Efficient multiunit auctions for normal goods

“…Thus, it is natural to ask whether the positive result from Theorem extends to a setting without symmetry of bidder preferences. In the of a working paper version of this paper, Baisa (), I show that it is a straightforward exercise to extend Theorem to a setting where bidders are ex‐ante asymmetric. In particular, I show that we can construct a nearly identical transformation maps that arbitrary cut‐off rule for bidder 1 to a more efficient cut‐off rule for bidder 1.…”

“…Instead the dimensionality of bidder's private information determines whether efficient implementation is possible. Toward this point, in a working paper version of this paper, Baisa (), gives a numerical example of an efficient auction that is dominant strategy incentive compatible when bidders have private budgets and single‐dimensional private information.…”

“…I study deviations from initial wealth because this allows a more flexible interpretation of the model where we can also include wealth as an element of bidders' private information. A working paper version of this paper, Baisa (), provides an example of an efficient mechanism where a bidder's wealth (her soft budget) varies with her private type.…”

“… A working paper version of this paper, Baisa (), gives a numerical example to show how we can explicitly construct such an efficient mechanism for the case where bidders have soft budgets. …”

Mechanism design without quasilinearity

“…The broad conclusion of this literature is that in a variety of problems, dominant strategy incentive compatibility, individual rationality, and efficiency (along with some other mild axioms) are incompatible without quasilinearity. The literature also identifies problems where these properties are compatible: see, for instance, Saitoh and Serizawa (), Hashimoto and Saitoh (), Morimoto and Serizawa (), Kazumura and Serizawa (), Zhou and Serizawa (), Baisa (), Ma et al () and references therein.…”