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Myerson's seminal work provides a computationally efficient revenue-optimal auction for selling one item to multiple bidders [17]. Generalizing this work to selling multiple items at once has been a central question in economics and algorithmic game theory, but its complexity has remained poorly understood. We answer this question by showing that a… (More)

Optimal mechanisms have been provided in quite general multi-item settings [Cai et al. 2012b, 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, e.g. when the bidders have additive valuations with independent and/or continuous values for the… (More)

We provide a duality-based framework for revenue maximization in a multiple-good monopoly. Our framework shows that every optimal mechanism has a certificate of optimality, taking the form of an optimal transportation map between measures. Using our framework, we prove that grand-bundling mechanisms are optimal if and only if two stochastic dominance… (More)

We study Facility Location games, where a number of facilities are placed in a metric space based on locations reported by strategic agents. A mechanism maps the agents' locations to a set of facilities. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility , and may misreport their location.… (More)

We consider <i>K</i>-Facility Location games, where <i>n</i> strategic agents report their locations in a metric space and a mechanism maps them to <i>K</i> facilities. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility, and may misreport their location. We are interested in deterministic… (More)

An (<i>n</i>,<i>k</i>)-<em>Poisson Multinomial Distribution</em> (PMD) is the distribution of the sum of <i>n</i> independent random vectors supported on the set <b> </b><i>B</i><sub><i>k</i></sub>={<i>e</i><sub>1</sub>,…,<i>e</i><sub><i>k</i></sub>} of standard basis vectors in ℝ<sup><i>k</i></sup>. We show that any… (More)

We show that computing the revenue-optimal deterministic auction in unit-demand single-buyer Bayesian settings, i.e. the optimal item-pricing, is computationally hard even in single-item settings where the buyer's value distribution is a sum of independently distributed attributes , or multi-item settings where the buyer's values for the items are… (More)

An (n, k)-Poisson Multinomial Distribution (PMD) is the distribution of the sum of n independent random vectors supported on the set B k = {e 1 ,. .. , e k } of standard basis vectors in R k. We prove a structural characterization of these distributions, showing that, for all ε > 0, any (n, k)-Poisson multinomial random vector is ε-close, in total variation… (More)

We consider <i>k</i>-Facility Location games, where <i>n</i> strategic agents report their locations on the real line, and a mechanism maps them to <i>k</i> facilities. Each agent seeks to minimize his connection cost, given by a nonnegative increasing function of his distance to the nearest facility. Departing from previous work, that mostly considers the… (More)

In <i>k</i>-Facility Location games, <i>n</i> strategic agents report their locations on the real line and a mechanism maps them to <i>k</i> facilities. Each agent seeks to minimize her connection cost to the nearest facility and the mechanism should be strategyproof and approximately efficient. Facility Location games have received considerable attention… (More)