47 research outputs found
Budget Constrained Auctions with Heterogeneous Items
In this paper, we present the first approximation algorithms for the problem
of designing revenue optimal Bayesian incentive compatible auctions when there
are multiple (heterogeneous) items and when bidders can have arbitrary demand
and budget constraints. Our mechanisms are surprisingly simple: We show that a
sequential all-pay mechanism is a 4 approximation to the revenue of the optimal
ex-interim truthful mechanism with discrete correlated type space for each
bidder. We also show that a sequential posted price mechanism is a O(1)
approximation to the revenue of the optimal ex-post truthful mechanism when the
type space of each bidder is a product distribution that satisfies the standard
hazard rate condition. We further show a logarithmic approximation when the
hazard rate condition is removed, and complete the picture by showing that
achieving a sub-logarithmic approximation, even for regular distributions and
one bidder, requires pricing bundles of items. Our results are based on
formulating novel LP relaxations for these problems, and developing generic
rounding schemes from first principles. We believe this approach will be useful
in other Bayesian mechanism design contexts.Comment: Final version accepted to STOC '10. Incorporates significant reviewer
comment
How to Allocate R&D (and Other) Subsidies: An Experimentally Tested Policy Recommendation
This paper evaluates how R&D subsidies to the business sector are typically awarded. We identify two sources of ine_ciency: the selection based on a ranking of individual projects, rather than complete allocations, and the failure to induce competition among applicants in order to extract and use information about the necessary funding. In order to correct these ine_- ciencies we propose mechanisms that include some form of an auction in which applicants bid for subsidies. Our proposals are tested in a simulation and in controlled lab experiments. The results suggest that adopting our proposals may considerably improve the allocation
Budget Feasible Mechanisms
We study a novel class of mechanism design problems in which the outcomes are
constrained by the payments. This basic class of mechanism design problems
captures many common economic situations, and yet it has not been studied, to
our knowledge, in the past. We focus on the case of procurement auctions in
which sellers have private costs, and the auctioneer aims to maximize a utility
function on subsets of items, under the constraint that the sum of the payments
provided by the mechanism does not exceed a given budget. Standard mechanism
design ideas such as the VCG mechanism and its variants are not applicable
here. We show that, for general functions, the budget constraint can render
mechanisms arbitrarily bad in terms of the utility of the buyer. However, our
main result shows that for the important class of submodular functions, a
bounded approximation ratio is achievable. Better approximation results are
obtained for subclasses of the submodular functions. We explore the space of
budget feasible mechanisms in other domains and give a characterization under
more restricted conditions
How to Allocate R&D (and Other) Subsidies: An Experimentally Tested Policy Recommendation
This paper evaluates how R&D subsidies to the business sector are typically awarded. We identify two sources of ine_ciency: the selection based on a ranking of individual projects, rather than complete allocations, and the failure to induce competition among applicants in order to extract and use information about the necessary funding. In order to correct these ine_- ciencies we propose mechanisms that include some form of an auction in which applicants bid for subsidies. Our proposals are tested in a simulation and in controlled lab experiments. The results suggest that adopting our proposals may considerably improve the allocation.Research; Subsidies; Experimental Economics
Coverage, Matching, and Beyond: New Results on Budgeted Mechanism Design
We study a type of reverse (procurement) auction problems in the presence of
budget constraints. The general algorithmic problem is to purchase a set of
resources, which come at a cost, so as not to exceed a given budget and at the
same time maximize a given valuation function. This framework captures the
budgeted version of several well known optimization problems, and when the
resources are owned by strategic agents the goal is to design truthful and
budget feasible mechanisms, i.e. elicit the true cost of the resources and
ensure the payments of the mechanism do not exceed the budget. Budget
feasibility introduces more challenges in mechanism design, and we study
instantiations of this problem for certain classes of submodular and XOS
valuation functions. We first obtain mechanisms with an improved approximation
ratio for weighted coverage valuations, a special class of submodular functions
that has already attracted attention in previous works. We then provide a
general scheme for designing randomized and deterministic polynomial time
mechanisms for a class of XOS problems. This class contains problems whose
feasible set forms an independence system (a more general structure than
matroids), and some representative problems include, among others, finding
maximum weighted matchings, maximum weighted matroid members, and maximum
weighted 3D-matchings. For most of these problems, only randomized mechanisms
with very high approximation ratios were known prior to our results
Revenue Maximization and Ex-Post Budget Constraints
We consider the problem of a revenue-maximizing seller with m items for sale
to n additive bidders with hard budget constraints, assuming that the seller
has some prior distribution over bidder values and budgets. The prior may be
correlated across items and budgets of the same bidder, but is assumed
independent across bidders. We target mechanisms that are Bayesian Incentive
Compatible, but that are ex-post Individually Rational and ex-post budget
respecting. Virtually no such mechanisms are known that satisfy all these
conditions and guarantee any revenue approximation, even with just a single
item. We provide a computationally efficient mechanism that is a
-approximation with respect to all BIC, ex-post IR, and ex-post budget
respecting mechanisms. Note that the problem is NP-hard to approximate better
than a factor of 16/15, even in the case where the prior is a point mass
\cite{ChakrabartyGoel}. We further characterize the optimal mechanism in this
setting, showing that it can be interpreted as a distribution over virtual
welfare maximizers.
We prove our results by making use of a black-box reduction from mechanism to
algorithm design developed by \cite{CaiDW13b}. Our main technical contribution
is a computationally efficient -approximation algorithm for the algorithmic
problem that results by an application of their framework to this problem. The
algorithmic problem has a mixed-sign objective and is NP-hard to optimize
exactly, so it is surprising that a computationally efficient approximation is
possible at all. In the case of a single item (), the algorithmic problem
can be solved exactly via exhaustive search, leading to a computationally
efficient exact algorithm and a stronger characterization of the optimal
mechanism as a distribution over virtual value maximizers