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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)

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)

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract 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… (More)

We provide global convergence guarantees for the expectation-maximization (EM) algorithm applied to mixtures of two Gaussians with known covariance matrices. We show that EM converges geometrically to the correct mean vectors, and provide simple, closed-form expressions for the convergence rate. As a simple illustration, we show that in one dimension ten… (More)

- Dimitris Fotakis, Christos Tzamos
- Theor. Comput. Sci.
- 2010

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)

- Dimitris Fotakis, Christos Tzamos
- ACM Trans. Economics and Comput.
- 2013

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 efficient peer grading mechanism is proposed for grading the multitude of assignments in online courses. This novel approach is based on game theory and mechanism design. A set of assumptions and a mathematical model is ratified to simulate the dominant strategy behavior of students in a given mechanism. A benchmark function accounting for grade accuracy… (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)

- Dimitris Fotakis, Christos Tzamos
- Algorithmica
- 2013

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)

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)