Truthful approximation mechanisms for restricted combinatorial auctions

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios

Rheological Model for Wood

Wood as the most important natural and renewable building material plays an important role in the construction sector. Nevertheless, its hygroscopic character basically affects all related mechanical properties leading to degradation of material stiffness and strength over the service life. Accordingly, to attain reliable design of the timber structures, the influence of moisture evolution and the role of time- and moisture-dependent behaviors have to be taken into account. For this purpose, in the current study a 3D orthotropic elasto-plastic, visco-elastic, mechano-sorptive constitutive model for wood, with all material constants being defined as a function of moisture content, is presented. The corresponding numerical integration approach, with additive decomposition of the total strain is developed and implemented within the framework of the finite element method (FEM). Moreover to preserve a quadratic rate of asymptotic convergence the consistent tangent operator for the whole model is derived. Functionality and capability of the presented material model are evaluated by performing several numerical verification simulations of wood components under different combinations of mechanical loading and moisture variation. Additionally, the flexibility and universality of the introduced model to predict the mechanical behavior of different species are demonstrated by the analysis of a hybrid wood element. Furthermore, the proposed numerical approach is validated by comparisons of computational evaluations with experimental results.Comment: 37 pages, 13 figures, 10 table

Public projects, Boolean functions and the borders of Border's theorem

Border's theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian single-item environment, and it has several applications in economic and algorithmic mechanism design. All known generalizations of Border's theorem either restrict attention to relatively simple settings, or resort to approximation. This paper identifies a complexity-theoretic barrier that indicates, assuming standard complexity class separations, that Border's theorem cannot be extended significantly beyond the state-of-the-art. We also identify a surprisingly tight connection between Myerson's optimal auction theory, when applied to public project settings, and some fundamental results in the analysis of Boolean functions.Comment: Accepted to ACM EC 201

Bayesian Incentive Compatibility via Fractional Assignments

Very recently, Hartline and Lucier studied single-parameter mechanism design problems in the Bayesian setting. They proposed a black-box reduction that converted Bayesian approximation algorithms into Bayesian-Incentive-Compatible (BIC) mechanisms while preserving social welfare. It remains a major open question if one can find similar reduction in the more important multi-parameter setting. In this paper, we give positive answer to this question when the prior distribution has finite and small support. We propose a black-box reduction for designing BIC multi-parameter mechanisms. The reduction converts any algorithm into an eps-BIC mechanism with only marginal loss in social welfare. As a result, for combinatorial auctions with sub-additive agents we get an eps-BIC mechanism that achieves constant approximation.Comment: 22 pages, 1 figur

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