12,663 research outputs found
Efficiency Guarantees in Auctions with Budgets
In settings where players have a limited access to liquidity, represented in
the form of budget constraints, efficiency maximization has proven to be a
challenging goal. In particular, the social welfare cannot be approximated by a
better factor then the number of players. Therefore, the literature has mainly
resorted to Pareto-efficiency as a way to achieve efficiency in such settings.
While successful in some important scenarios, in many settings it is known that
either exactly one incentive-compatible auction that always outputs a
Pareto-efficient solution, or that no truthful mechanism can always guarantee a
Pareto-efficient outcome. Traditionally, impossibility results can be avoided
by considering approximations. However, Pareto-efficiency is a binary property
(is either satisfied or not), which does not allow for approximations.
In this paper we propose a new notion of efficiency, called \emph{liquid
welfare}. This is the maximum amount of revenue an omniscient seller would be
able to extract from a certain instance. We explain the intuition behind this
objective function and show that it can be 2-approximated by two different
auctions. Moreover, we show that no truthful algorithm can guarantee an
approximation factor better than 4/3 with respect to the liquid welfare, and
provide a truthful auction that attains this bound in a special case.
Importantly, the liquid welfare benchmark also overcomes impossibilities for
some settings. While it is impossible to design Pareto-efficient auctions for
multi-unit auctions where players have decreasing marginal values, we give a
deterministic -approximation for the liquid welfare in this setting
Auctions with Heterogeneous Items and Budget Limits
We study individual rational, Pareto optimal, and incentive compatible
mechanisms for auctions with heterogeneous items and budget limits. For
multi-dimensional valuations we show that there can be no deterministic
mechanism with these properties for divisible items. We use this to show that
there can also be no randomized mechanism that achieves this for either
divisible or indivisible items. For single-dimensional valuations we show that
there can be no deterministic mechanism with these properties for indivisible
items, but that there is a randomized mechanism that achieves this for either
divisible or indivisible items. The impossibility results hold for public
budgets, while the mechanism allows private budgets, which is in both cases the
harder variant to show. While all positive results are polynomial-time
algorithms, all negative results hold independent of complexity considerations
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
Composable and Efficient Mechanisms
We initiate the study of efficient mechanism design with guaranteed good
properties even when players participate in multiple different mechanisms
simultaneously or sequentially. We define the class of smooth mechanisms,
related to smooth games defined by Roughgarden, that can be thought of as
mechanisms that generate approximately market clearing prices. We show that
smooth mechanisms result in high quality outcome in equilibrium both in the
full information setting and in the Bayesian setting with uncertainty about
participants, as well as in learning outcomes. Our main result is to show that
such mechanisms compose well: smoothness locally at each mechanism implies
efficiency globally.
For mechanisms where good performance requires that bidders do not bid above
their value, we identify the notion of a weakly smooth mechanism. Weakly smooth
mechanisms, such as the Vickrey auction, are approximately efficient under the
no-overbidding assumption. Similar to smooth mechanisms, weakly smooth
mechanisms behave well in composition, and have high quality outcome in
equilibrium (assuming no overbidding) both in the full information setting and
in the Bayesian setting, as well as in learning outcomes.
In most of the paper we assume participants have quasi-linear valuations. We
also extend some of our results to settings where participants have budget
constraints
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