We study the classic mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known distribution. In single parameter settings (i.e., where each agent's preference is given by a single private value for being served and zero for not being served) this problem is solved [20]. Unfortunately, these single parameter optimal mechanisms are impractical and rarely employed [1], and furthermore the underlying economic theory fails to generalize to the important, relevant, and unsolved multi-dimensional setting (i.e., where each agent's preference is given by multiple values for each of the multiple services available) [25].In contrast to the theory of optimal mechanisms we develop a theory of sequential posted price mechanisms, where agents in sequence are offered take-it-or-leave-it prices. We prove that these mechanisms are approximately optimal in single-dimensional settings. These posted-price mechanisms avoid many of the properties of optimal mechanisms that make the latter impractical. Furthermore, these mechanisms generalize naturally to multi-dimensional settings where they give the first known approximations to the elusive optimal multi-dimensional mechanism design problem. In particular, we solve multi-dimensional multi-unit auction problems and generalizations to matroid feasibility constraints. The constant approximations we obtain range from 1.5 to 8. For all but one case, our posted price sequences can be computed in polynomial time.This work can be viewed as an extension and improvement of the single-agent algorithmic pricing work of [9] to the setting of multiple agents where the designer has combinatorial feasibility constraints on which agents can simultaneously obtain each service.

We investigate the power of randomness in the context of a fundamental Bayesian optimal mechanism design problem-a single seller aims to maximize expected revenue by allocating multiple kinds of resources to "unit-demand" agents with preferences drawn from a known distribution. When the agents' preferences are single-dimensional Myerson's seminal work [14] shows that randomness offers no benefit-the optimal mechanism is always deterministic. In the multi-dimensional case, where each agent's preferences are given by different values for each of the available services, Briest et al. [7] recently showed that the gap between the expected revenue obtained by an optimal randomized mechanism and an optimal deterministic mechanism can be unbounded even when a single agent is offered only 4 services. However, this large gap is attained through unnatural instances where values of the agent for different services are correlated in a specific way. We show that when the agent's values involve no correlation or a specific kind of positive correlation, the benefit of randomness is only a small constant factor (4 and 8 respectively). Our model of positively correlated values (that we call additive values) is a natural model for unit-demand agents and items that are substitutes. Our results extend to multiple agent settings as well.

The aim of this paper is to present a method for modeling the lifespan of insulation materials in a partial discharge regime. Based on the design of experiments, it has many advantages: it reduces the number of time-consuming experiments, increases the accuracy of the results and allows lifespan modeling under various stress conditions including coupling effects between the factors. Accelerated aging tests are carried out to determine the lifespan of these materials. The resulting model presents an original relationship between the logarithm of the insulation lifespan and that of electrically applied stress and an exponential form of the temperature. Results show that the most influential factors can be identified according to their effects on the insulation lifespan. Moreover, the lifespan model validity is tested either with additional points which have not been used for modeling or through statistical tests. Finally, it is shown that fractional plans are not suitable to r e d u c e t h e n u m b e r o f e x p e r i m e n t s. T h i s a p p l i c a t i o n o f t h e experimental design is best used during the initial phase, before the final drive has been built and any on-line diagnostic.