Budget Feasible Mechanism Design: From Prior-Free to Bayesian

Budget feasible mechanism design studies procurement combinatorial auctions where the sellers have private costs to produce items, and the buyer(auctioneer) aims to maximize a social valuation function on subsets of items, under the budget constraint on the total payment. One of the most important questions in the field is "which valuation domains admit truthful budget feasible mechanisms with `small' approximations (compared to the social optimum)?" Singer showed that additive and submodular functions have such constant approximations. Recently, Dobzinski, Papadimitriou, and Singer gave an O(log^2 n)-approximation mechanism for subadditive functions; they also remarked that: "A fundamental question is whether, regardless of computational constraints, a constant-factor budget feasible mechanism exists for subadditive functions." We address this question from two viewpoints: prior-free worst case analysis and Bayesian analysis. For the prior-free framework, we use an LP that describes the fractional cover of the valuation function; it is also connected to the concept of approximate core in cooperative game theory. We provide an O(I)-approximation mechanism for subadditive functions, via the worst case integrality gap I of LP. This implies an O(log n)-approximation for subadditive valuations, O(1)-approximation for XOS valuations, and for valuations with a constant I. XOS valuations are an important class of functions that lie between submodular and subadditive classes. We give another polynomial time O(log n/loglog n) sub-logarithmic approximation mechanism for subadditive valuations. For the Bayesian framework, we provide a constant approximation mechanism for all subadditive functions, using the above prior-free mechanism for XOS valuations as a subroutine. Our mechanism allows correlations in the distribution of private information and is universally truthful.Comment: to appear in STOC 201

Chain: A Dynamic Double Auction Framework for Matching Patient Agents

In this paper we present and evaluate a general framework for the design of truthful auctions for matching agents in a dynamic, two-sided market. A single commodity, such as a resource or a task, is bought and sold by multiple buyers and sellers that arrive and depart over time. Our algorithm, Chain, provides the first framework that allows a truthful dynamic double auction (DA) to be constructed from a truthful, single-period (i.e. static) double-auction rule. The pricing and matching method of the Chain construction is unique amongst dynamic-auction rules that adopt the same building block. We examine experimentally the allocative efficiency of Chain when instantiated on various single-period rules, including the canonical McAfee double-auction rule. For a baseline we also consider non-truthful double auctions populated with zero-intelligence plus"-style learning agents. Chain-based auctions perform well in comparison with other schemes, especially as arrival intensity falls and agent valuations become more volatile

Selling Privacy at Auction

We initiate the study of markets for private data, though the lens of differential privacy. Although the purchase and sale of private data has already begun on a large scale, a theory of privacy as a commodity is missing. In this paper, we propose to build such a theory. Specifically, we consider a setting in which a data analyst wishes to buy information from a population from which he can estimate some statistic. The analyst wishes to obtain an accurate estimate cheaply. On the other hand, the owners of the private data experience some cost for their loss of privacy, and must be compensated for this loss. Agents are selfish, and wish to maximize their profit, so our goal is to design truthful mechanisms. Our main result is that such auctions can naturally be viewed and optimally solved as variants of multi-unit procurement auctions. Based on this result, we derive auctions for two natural settings which are optimal up to small constant factors: 1. In the setting in which the data analyst has a fixed accuracy goal, we show that an application of the classic Vickrey auction achieves the analyst's accuracy goal while minimizing his total payment. 2. In the setting in which the data analyst has a fixed budget, we give a mechanism which maximizes the accuracy of the resulting estimate while guaranteeing that the resulting sum payments do not exceed the analysts budget. In both cases, our comparison class is the set of envy-free mechanisms, which correspond to the natural class of fixed-price mechanisms in our setting. In both of these results, we ignore the privacy cost due to possible correlations between an individuals private data and his valuation for privacy itself. We then show that generically, no individually rational mechanism can compensate individuals for the privacy loss incurred due to their reported valuations for privacy.Comment: Extended Abstract appeared in the proceedings of EC 201