23,650 research outputs found
On the Ratio of Revenue to Welfare in Single-Parameter Mechanism Design
What fraction of the potential social surplus in an environment can be
extracted by a revenue-maximizing monopolist? We investigate this problem in
Bayesian single-parameter environments with independent private values. The
precise answer to the question obviously depends on the particulars of the
environment: the feasibility constraint and the distributions from which the
bidders' private values are sampled. Rather than solving the problem in
particular special cases, our work aims to provide universal lower bounds on
the revenue-to-welfare ratio that hold under the most general hypotheses that
allow for non-trivial such bounds.
Our results can be summarized as follows. For general feasibility
constraints, the revenue-to-welfare ratio is at least a constant times the
inverse-square-root of the number of agents, and this is tight up to constant
factors. For downward-closed feasibility constraints, the revenue-to-welfare
ratio is bounded below by a constant. Both results require the bidders'
distributions to satisfy hypotheses somewhat stronger than regularity; we show
that the latter result cannot avoid this requirement.Comment: 15 page
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
Prophet Inequalities with Limited Information
In the classical prophet inequality, a gambler observes a sequence of
stochastic rewards and must decide, for each reward ,
whether to keep it and stop the game or to forfeit the reward forever and
reveal the next value . The gambler's goal is to obtain a constant
fraction of the expected reward that the optimal offline algorithm would get.
Recently, prophet inequalities have been generalized to settings where the
gambler can choose items, and, more generally, where he can choose any
independent set in a matroid. However, all the existing algorithms require the
gambler to know the distribution from which the rewards are
drawn.
The assumption that the gambler knows the distribution from which
are drawn is very strong. Instead, we work with the much simpler
assumption that the gambler only knows a few samples from this distribution. We
construct the first single-sample prophet inequalities for many settings of
interest, whose guarantees all match the best possible asymptotically,
\emph{even with full knowledge of the distribution}. Specifically, we provide a
novel single-sample algorithm when the gambler can choose any elements
whose analysis is based on random walks with limited correlation. In addition,
we provide a black-box method for converting specific types of solutions to the
related \emph{secretary problem} to single-sample prophet inequalities, and
apply it to several existing algorithms. Finally, we provide a constant-sample
prophet inequality for constant-degree bipartite matchings.
We apply these results to design the first posted-price and multi-dimensional
auction mechanisms with limited information in settings with asymmetric
bidders
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
Reallocation Mechanisms
We consider reallocation problems in settings where the initial endowment of
each agent consists of a subset of the resources. The private information of
the players is their value for every possible subset of the resources. The goal
is to redistribute resources among agents to maximize efficiency. Monetary
transfers are allowed, but participation is voluntary.
We develop incentive-compatible, individually-rational and budget balanced
mechanisms for several classic settings, including bilateral trade, partnership
dissolving, Arrow-Debreu markets, and combinatorial exchanges. All our
mechanisms (except one) provide a constant approximation to the optimal
efficiency in these settings, even in ones where the preferences of the agents
are complex multi-parameter functions
- …