ﻻ يوجد ملخص باللغة العربية
We study a central problem in Algorithmic Mechanism Design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that guarantees a non-trivial approximation ratio of $O(log^2 m)$ [STOC06], where $m$ is the number of items. This was subsequently improved to $O(log mlog log m)$ [Dobzinski, APPROX07] and then to $O(log m)$ [Krysta and Vocking, ICALP12]. In this paper we develop the first mechanism that breaks the logarithmic barrier. Specifically, the mechanism provides an approximation ratio of $O(sqrt {log m})$. Similarly to previous constructions, our mechanism uses polynomially many value and demand queries, and in fact provides the same approximation ratio for the larger class of XOS (a.k.a. fractionally subadditive) valuations. We also develop a computationally efficient implementation of the mechanism for combinatorial auctions with budget additive bidders. Although in general computing a demand query is NP-hard for budget additive valuations, we observe that the specific form of demand queries that our mechanism uses can be efficiently computed when bidders are budget additive.
We provide the first separation in the approximation guarantee achievable by truthful and non-truthful combinatorial auctions with polynomial communication. Specifically, we prove that any truthful mechanism guaranteeing a $(frac{3}{4}-frac{1}{240}+v
A seminal result of Bulow and Klemperer [1989] demonstrates the power of competition for extracting revenue: when selling a single item to $n$ bidders whose values are drawn i.i.d. from a regular distribution, the simple welfare-maximizing VCG mechan
In this note we study the greedy algorithm for combinatorial auctions with submodular bidders. It is well known that this algorithm provides an approximation ratio of $2$ for every order of the items. We show that if the valuations are vertex cover f
We study the problem of selling a good to a group of bidders with interdependent values in a prior-free setting. Each bidder has a signal that can take one of $k$ different values, and her value for the good is a weakly increasing function of all the
We study combinatorial auctions with bidders that exhibit endowment effect. In most of the previous work on cognitive biases in algorithmic game theory (e.g., [Kleinberg and Oren, EC14] and its follow-ups) the focus was on analyzing the implications