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Consider a monopolist selling $n$ items to an additive buyer whose item values are drawn from independent distributions $F_1,F_2,ldots,F_n$ possibly having unbounded support. Unlike in the single-item case, it is well known that the revenue-optimal selling mechanism (a pricing scheme) may be complex, sometimes requiring a continuum of menu entries. Also known is that simple mechanisms with a bounded number of menu entries can extract a constant fraction of the optimal revenue. Nonetheless, whether an arbitrarily high fraction of the optimal revenue can be extracted via a bounded menu size remained open. We give an affirmative answer: for every $n$ and $varepsilon>0$, there exists $C=C(n,varepsilon)$ s.t. mechanisms of menu size at most $C$ suffice for obtaining $(1-varepsilon)$ of the optimal revenue from any $F_1,ldots,F_n$. We prove upper and lower bounds on the revenue-approximation complexity $C(n,varepsilon)$ and on the deterministic communication complexity required to run a mechanism achieving such an approximation.
The question of the minimum menu-size for approximate (i.e., up-to-$varepsilon$) Bayesian revenue maximization when selling two goods to an additive risk-neutral quasilinear buyer was introduced by Hart and Nisan (2013), who give an upper bound of $O
We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of $n$ additive bidders whose values for $m$ heterogeneous items are drawn independen
We analyze the revenue loss due to market shrinkage. Specifically, consider a simple market with one item for sale and $n$ bidders whose values are drawn from some joint distribution. Suppose that the market shrinks as a single bidder retires from th
We investigate revenue guarantees for auction mechanisms in a model where a distribution is specified for each bidder, but only some of the distributions are correct. The subset of bidders whose distribution is correctly specified (henceforth, the gr
Most work in mechanism design assumes that buyers are risk neutral; some considers risk aversion arising due to a non-linear utility for money. Yet behavioral studies have established that real agents exhibit risk attitudes which cannot be captured b