1,920 research outputs found
Truthful Mechanisms for Agents that Value Privacy
Recent work has constructed economic mechanisms that are both truthful and
differentially private. In these mechanisms, privacy is treated separately from
the truthfulness; it is not incorporated in players' utility functions (and
doing so has been shown to lead to non-truthfulness in some cases). In this
work, we propose a new, general way of modelling privacy in players' utility
functions. Specifically, we only assume that if an outcome has the property
that any report of player would have led to with approximately the same
probability, then has small privacy cost to player . We give three
mechanisms that are truthful with respect to our modelling of privacy: for an
election between two candidates, for a discrete version of the facility
location problem, and for a general social choice problem with discrete
utilities (via a VCG-like mechanism). As the number of players increases,
the social welfare achieved by our mechanisms approaches optimal (as a fraction
of )
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
Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round
Many algorithms that are originally designed without explicitly considering
incentive properties are later combined with simple pricing rules and used as
mechanisms. The resulting mechanisms are often natural and simple to
understand. But how good are these algorithms as mechanisms? Truthful reporting
of valuations is typically not a dominant strategy (certainly not with a
pay-your-bid, first-price rule, but it is likely not a good strategy even with
a critical value, or second-price style rule either). Our goal is to show that
a wide class of approximation algorithms yields this way mechanisms with low
Price of Anarchy.
The seminal result of Lucier and Borodin [SODA 2010] shows that combining a
greedy algorithm that is an -approximation algorithm with a
pay-your-bid payment rule yields a mechanism whose Price of Anarchy is
. In this paper we significantly extend the class of algorithms for
which such a result is available by showing that this close connection between
approximation ratio on the one hand and Price of Anarchy on the other also
holds for the design principle of relaxation and rounding provided that the
relaxation is smooth and the rounding is oblivious.
We demonstrate the far-reaching consequences of our result by showing its
implications for sparse packing integer programs, such as multi-unit auctions
and generalized matching, for the maximum traveling salesman problem, for
combinatorial auctions, and for single source unsplittable flow problems. In
all these problems our approach leads to novel simple, near-optimal mechanisms
whose Price of Anarchy either matches or beats the performance guarantees of
known mechanisms.Comment: Extended abstract appeared in Proc. of 16th ACM Conference on
Economics and Computation (EC'15
Truthful Learning Mechanisms for Multi-Slot Sponsored Search Auctions with Externalities
Sponsored search auctions constitute one of the most successful applications
of microeconomic mechanisms. In mechanism design, auctions are usually designed
to incentivize advertisers to bid their truthful valuations and to assure both
the advertisers and the auctioneer a non-negative utility. Nonetheless, in
sponsored search auctions, the click-through-rates (CTRs) of the advertisers
are often unknown to the auctioneer and thus standard truthful mechanisms
cannot be directly applied and must be paired with an effective learning
algorithm for the estimation of the CTRs. This introduces the critical problem
of designing a learning mechanism able to estimate the CTRs at the same time as
implementing a truthful mechanism with a revenue loss as small as possible
compared to an optimal mechanism designed with the true CTRs. Previous work
showed that, when dominant-strategy truthfulness is adopted, in single-slot
auctions the problem can be solved using suitable exploration-exploitation
mechanisms able to achieve a per-step regret (over the auctioneer's revenue) of
order (where T is the number of times the auction is repeated).
It is also known that, when truthfulness in expectation is adopted, a per-step
regret (over the social welfare) of order can be obtained. In
this paper we extend the results known in the literature to the case of
multi-slot auctions. In this case, a model of the user is needed to
characterize how the advertisers' valuations change over the slots. We adopt
the cascade model that is the most famous model in the literature for sponsored
search auctions. We prove a number of novel upper bounds and lower bounds both
on the auctioneer's revenue loss and social welfare w.r.t. to the VCG auction
and we report numerical simulations investigating the accuracy of the bounds in
predicting the dependency of the regret on the auction parameters
Computational Efficiency Requires Simple Taxation
We characterize the communication complexity of truthful mechanisms. Our
departure point is the well known taxation principle. The taxation principle
asserts that every truthful mechanism can be interpreted as follows: every
player is presented with a menu that consists of a price for each bundle (the
prices depend only on the valuations of the other players). Each player is
allocated a bundle that maximizes his profit according to this menu. We define
the taxation complexity of a truthful mechanism to be the logarithm of the
maximum number of menus that may be presented to a player.
Our main finding is that in general the taxation complexity essentially
equals the communication complexity. The proof consists of two main steps.
First, we prove that for rich enough domains the taxation complexity is at most
the communication complexity. We then show that the taxation complexity is much
smaller than the communication complexity only in "pathological" cases and
provide a formal description of these extreme cases.
Next, we study mechanisms that access the valuations via value queries only.
In this setting we establish that the menu complexity -- a notion that was
already studied in several different contexts -- characterizes the number of
value queries that the mechanism makes in exactly the same way that the
taxation complexity characterizes the communication complexity.
Our approach yields several applications, including strengthening the
solution concept with low communication overhead, fast computation of prices,
and hardness of approximation by computationally efficient truthful mechanisms
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