1,338 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
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
Pricing Ad Slots with Consecutive Multi-unit Demand
We consider the optimal pricing problem for a model of the rich media
advertisement market, as well as other related applications. In this market,
there are multiple buyers (advertisers), and items (slots) that are arranged in
a line such as a banner on a website. Each buyer desires a particular number of
{\em consecutive} slots and has a per-unit-quality value (dependent on
the ad only) while each slot has a quality (dependent on the position
only such as click-through rate in position auctions). Hence, the valuation of
the buyer for item is . We want to decide the allocations and
the prices in order to maximize the total revenue of the market maker.
A key difference from the traditional position auction is the advertiser's
requirement of a fixed number of consecutive slots. Consecutive slots may be
needed for a large size rich media ad. We study three major pricing mechanisms,
the Bayesian pricing model, the maximum revenue market equilibrium model and an
envy-free solution model. Under the Bayesian model, we design a polynomial time
computable truthful mechanism which is optimum in revenue. For the market
equilibrium paradigm, we find a polynomial time algorithm to obtain the maximum
revenue market equilibrium solution. In envy-free settings, an optimal solution
is presented when the buyers have the same demand for the number of consecutive
slots. We conduct a simulation that compares the revenues from the above
schemes and gives convincing results.Comment: 27page
Revenue maximizing envy-free fixed-price auctions with budgets
Traditional incentive-compatible auctions [6,16] for selling multiple goods to unconstrained and budgeted bidders can discriminate between bidders by selling identical goods at different prices. For this reason, Feldman et al. [7] dropped incentive compatibility and turned the attention to revenue maximizing envy-free item-pricing allocations for budgeted bidders. Envy-free allocations were suggested by classical papers [9,15]. The key property of such allocations is that no one envies the allocation and the price charged to anyone else. In this paper we consider this classical notion of envy-freeness and study fixed-price mechanisms which use nondiscriminatory uniform prices for all goods. Feldman et al. [7] gave an item-pricing mechanism that obtains 1/2 of the revenue obtained from any envy-free fixed-price mechanism for identical goods. We improve over this result by presenting an FPTAS for the problem that returns an (1 − ε)-approximation of the revenue obtained by any envy-free fixed-price mechanism for any ε > 0 and runs in polynomial time in the number of bidders n and 1/ ε even for exponential supply of goods m. Next, we consider the case of budgeted bidders with matching-type preferences on the set of goods, i.e., the valuation of each bidder for each item is either v i or 0. In this more general case, we prove that it is impossible to approximate the optimum revenue within O( min (n,m)1/2 − ε ) for any ε > 0 unless P = NP. On the positive side, we are able to extend the FPTAS for identical goods to budgeted bidders in the case of constant number of different types of goods. Our FPTAS gives also a constant approximation with respect to the general envy-free auction
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