Related papers: Mechanism Design via Optimal Transport
We provide sufficient conditions for revenue maximization in a two-good monopoly where the buyer's values for the items come from independent (but not necessarily identical) distributions over bounded intervals. Under certain distributional…
Myerson's seminal characterization of the revenue-optimal auction for a single item \cite{myerson1981optimal} remains a cornerstone of mechanism design. However, generalizing this framework to multi-item settings has proven exceptionally…
We consider optimal mechanism design for the case with one buyer and two items. The buyer's valuations towards the two items are independent and additive. In this setting, optimal mechanism is unknown for general valuation distributions. We…
Using duality theory techniques we derive simple, closed-form formulas for bounding the optimal revenue of a monopolist selling many heterogeneous goods, in the case where the buyer's valuations for the items come i.i.d. from a uniform…
We study the problem of designing optimal auctions under restrictions on the set of permissible allocations. In addition to allowing us to restrict to deterministic mechanisms, we can also indirectly model non-additive valuations. We prove…
An indivisible object may be sold to one of $n$ agents who know their valuations of the object. The seller would like to use a revenue-maximizing mechanism but her knowledge of the valuations' distribution is scarce: she knows only the…
We characterize optimal mechanisms for the multiple-good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measure $\mu$ derived from the buyer's type distribution satisfies certain…
We study a seller who sells a single good to multiple bidders with uncertainty over the joint distribution of bidders' valuations, as well as bidders' higher-order beliefs about their opponents. The seller only knows the (possibly…
We consider the design of a revenue-optimal mechanism when two items are available to be sold to a single buyer whose valuation is uniformly distributed over an arbitrary rectangle $[c_1,c_1+b_1]\times[c_2,c_2+b_2]$ in the positive…
We introduce a dynamic mechanism design problem in which the designer wants to offer for sale an item to an agent, and another item to the same agent at some point in the future. The agent's joint distribution of valuations for the two…
We efficiently solve the optimal multi-dimensional mechanism design problem for independent bidders with arbitrary demand constraints when either the number of bidders is a constant or the number of items is a constant. In the first…
In multi-item screening, optimal selling mechanisms are challenging to characterize and implement, even with full knowledge of valuation distributions. In this paper, we aim to develop tractable, interpretable, and implementable mechanisms…
We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the…
We consider the problem of designing a revenue-optimal mechanism in the two-item, single-buyer, unit-demand setting when the buyer's valuations, $(z_1, z_2)$, are uniformly distributed in an arbitrary rectangle $[c,c+b_1]\times[c,c+b_2]$ in…
We study robustly optimal mechanisms for selling multiple items. The seller maximizes revenue against a worst-case distribution of a buyer's valuations within a set of distributions, called an "ambiguity" set. We identify the exact forms of…
Finding the optimal (revenue-maximizing) mechanism to sell multiple items has been a prominent and notoriously difficult open problem. Existing work has mainly focused on deriving analytical results tailored to a particular class of…
Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major…
We consider revenue-optimal mechanism design in the interdimensional setting, where one dimension is the 'value' of the buyer, and one is a 'type' that captures some auxiliary information. One setting is the FedEx Problem, for which FGKK…
We consider a monopolist seller facing a single buyer with additive valuations over n heterogeneous, independent items. It is known that in this important setting optimal mechanisms may require randomization [HR12], use menus of infinite…
Myerson's seminal work provides a computationally efficient revenue-optimal auction for selling one item to multiple bidders. Generalizing this work to selling multiple items at once has been a central question in economics and algorithmic…