Related papers: Selling Two Goods Optimally
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 provide a new, much simplified and straightforward proof to a result of Pavlov [2011] regarding the revenue maximizing mechanism for selling two goods with uniformly i.i.d. valuations over intervals $[c,c+1]$, to an additive buyer. This…
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…
It is well-known that optimal (i.e., revenue-maximizing) selling mechanisms in multidimensional type spaces may involve randomization. We obtain conditions under which deterministic mechanisms are optimal for selling two identical,…
Optimal mechanisms have been provided in quite general multi-item settings, as long as each bidder's type distribution is given explicitly by listing every type in the support along with its associated probability. In the implicit setting,…
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 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…
A seller is selling a pair of divisible complementary goods to an agent. The agent consumes the goods only in a specific ratio and freely disposes of excess in either goods. The value of the bundle and the ratio are private information of…
Maximizing the revenue from selling _more than one_ good (or item) to a single buyer is a notoriously difficult problem, in stark contrast to the one-good case. For two goods, we show that simple "one-dimensional" mechanisms, such as…
We study revenue maximization by deterministic mechanisms for the simplest case for which Myerson's characterization does not hold: a single seller selling two items, with independently distributed values, to a single additive buyer. We…
A monopolistic seller aims to sell an indivisible item to multiple potential buyers. Each buyer's valuation depends on their private type and the item's quality. The seller can observe the quality but it is unknown to buyers. This quality…
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…
We consider a monopolist seller with $n$ heterogeneous items, facing a single buyer. The buyer has a value for each item drawn independently according to (non-identical) distributions, and her value for a set of items is additive. 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…
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 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 provide an elementary proof that revenue-maximizing mechanisms exist in multi-parameter settings whenever the distribution of valuations has finite expectation.
We apply marginal analysis \`a la Bulow and Roberts (1989) to characterize revenue-maximizing selling mechanisms for a multiproduct monopoly. We derive marginal revenue from price perturbations over arbitrary sets of bundles and show that…
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…