منابع مشابه
Identifying combinatorial valuations from aggregate demand
We study identification of combinatorial valuations from aggregate demand. Each utility function takes as arguments subsets or, alternatively, quantities of the multiple goods. We exploit mathematical insights from auction theory to generically identify the distribution of utility functions. In our setting, aggregate demand for each item is observable while demand for bundles is not. Neverthele...
متن کاملCombinatorial Auctions with k-wise Dependent Valuations
We analyze the computational and communication complexity of combinatorial auctions from a new perspective: the degree of interdependency between the items for sale in the bidders’ preferences. Denoting by Gk the class of valuations displaying up to k-wise dependencies, we consider the hierarchy G1 ⊂ G2 ⊂ · · · ⊂ Gm, where m is the number of items for sale. We show that the minimum non-trivial ...
متن کاملStar Valuations and Dual Mixed Volumes
Since its creation by Brunn and Minkowski, what has become known as the Brunn Minkowski theory has provided powerful machinery to solve a broad variety of inverse problems with stereological data. The machinery of the Brunn Minkowski theory includes mixed volumes (of Minkowski), symmetrization techniques (such as those of Steiner and Blaschke), isoperimetric inequalities (such as the Brunn Mink...
متن کاملCommunication Complexity of Combinatorial Auctions with Submodular Valuations
We prove the first communication complexity lower bound for constant-factor approximation of the submodular welfare problem. More precisely, we show that a (1− 1 2e+ )-approximation (' 0.816) for welfare maximization in combinatorial auctions with submodular valuations would require exponential communication. We also show NP-hardness of (1− 1 2e+ )approximation in a computational model where ea...
متن کاملOnline Appendix for “Identifying Combinatorial Valuations from Aggregate Demand”
This Online Appendix addresses several issues mentioned but not discussed in depth in the paper. Section I discusses various extensions of the basic model. Section II shows that for our identification arguments, it is sufficient to observe aggregate demand where it is singlevalued. Section III provides a proof of part 3 of Proposition 4. Section IV provides an example that shows that the set of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2017
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.08.032