Optimal Pricing Is Hard

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 independent. We also show that it is intractable to optimally price the grand bundle of multiple items for an additive bidder whose values for the items are independent. These difficulties stem from implicit definitions of a value distribution. We provide three instances of how different properties of implicit distributions can lead to intractability: the first is a #P-hardness proof, while the remaining two are reductions from the SQRT-SUM problem of Garey, Graham, and Johnson [14]. While simple pricing schemes can oftentimes approximate the best scheme in revenue, they can have drastically different underlying structure. We argue therefore that either the specification of the input distribution must be highly restricted in format, or it is necessary for the goal to be mere approximation to the optimal scheme’s revenue instead of computing properties of the scheme itself.Microsoft Research (Fellowship)Alfred P. Sloan Foundation (Fellowship)National Science Foundation (U.S.) (CAREER Award CCF-0953960)National Science Foundation (U.S.) (Award CCF-1101491)Hertz Foundation (Daniel Stroock Fellowship

Sampling and Representation Complexity of Revenue Maximization

We consider (approximate) revenue maximization in auctions where the distribution on input valuations is given via "black box" access to samples from the distribution. We observe that the number of samples required -- the sample complexity -- is tightly related to the representation complexity of an approximately revenue-maximizing auction. Our main results are upper bounds and an exponential lower bound on these complexities

Influencia de las aleaciones metálicas en el color de la cerámica

El efecto cromático final de las restauraciones metalo-cerámicas se ve influenciado por el tipo de aleación metálica usada en su realización. En este estudio hemos realizado un análisis calorimétrico de 50 especímenes donde se combinan dos colores y cinco aleaciones diferentes. Después del análisis estadístico pertinente, se ha concluido que las aleaciones de base paladio plata son las que producen una variación más notoria del color, aumentando la saturación de amarillo y verde

Lake Ohrid, Albania, provides an exceptional multi-proxy record of environmental changes during the last glacial-interglacial cycle

Multi-proxy analyses on core JO2004-1 recovered from Lake Ohrid (40°55.000 N, 20°40.297E, 705 m a.s.l.) provide the first environmental and climate reconstruction in a mountainous area in Southern Europe over the last 140,000 years. The response of both lacustrine and terrestrial environments to climate change has been amplified by the peculiar geomorphological and hydrological setting, with a steep altitudinal gradient in the catchment and a karstic system feeding the lake. The karstic system was active during interglacials, leading to high carbonate production in the lake, and blocked during glacials as a result of extremely cold climate conditions with permafrost in the mountains. At the Riss–Eemian transition (Termination 2) the increase in lacustrine productivity predated forest expansion by about 10,000 years. In contrast, the Late Glacial–Holocene transition (Termination 1) was characterized by the dramatic impact of the Younger Dryas, which initially prevented interglacial carbonate production and delayed its maximum until the mid- Holocene. In contrast, forest expansion was progressive, starting as early as ca. 38,000 ago. The proximity of high mountains and the probable moderating lake effect on local climate conditions promoted forest expansion, and contributed to make the surroundings of Lake Ohrid favourable to forest refugia during the last glacial, usually steppic, period. Our study of sedimentology, mineralogy, geochemistry, magnetics, palynology and isotopes illustrates the non-linear response of terrestrial and lacustrine ecosystems to similar climate events, and demonstrates the potential of Lake Ohrid as an excellent paleoclimatic archive during the Quaternary