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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 $O(frac{1}{varepsilon^4})$ for this problem. Using the optimal-transport duality framework of Daskalakis et al. (2013, 2015), we derive the first lower bound for this problem - of $Omega(frac{1}{sqrt[4]{varepsilon}})$, even when the values for the two goods are drawn i.i.d. from nice distributions, establishing how to reason about approximately optimal mechanisms via this duality framework. This bound implies, for any fixed number of goods, a tight bound of $Theta(logfrac{1}{varepsilon})$ on the minimum deterministic communication complexity guaranteed to suffice for running some approximately revenue-maximizing mechanism, thereby completely resolving this problem. As a secondary result, we show that under standard economic assumptions on distributions, the above upper bound of Hart and Nisan (2013) can be strengthened to $O(frac{1}{varepsilon^2})$.
We identify the first static credible mechanism for multi-item additive auctions that achieves a constant factor of the optimal revenue. This is one instance of a more general framework for designing two-part tariff auctions, adapting the duality fra
This paper develops a general approach, rooted in statistical learning theory, to learning an approximately revenue-maximizing auction from data. We introduce $t$-level auctions to interpolate between simple auctions, such as welfare maximization wit
We study the design of a decentralized two-sided matching market in which agents search is guided by the platform. There are finitely many agent types, each with (potentially random) preferences drawn from known type-specific distributions. Equipped
Mechanism design for one-sided markets has been investigated for several decades in economics and in computer science. More recently, there has been an increased attention on mechanisms for two-sided markets, in which buyers and sellers act strategic
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 s