21 research outputs found
Valuation Compressions in VCG-Based Combinatorial Auctions
The focus of classic mechanism design has been on truthful direct-revelation
mechanisms. In the context of combinatorial auctions the truthful
direct-revelation mechanism that maximizes social welfare is the VCG mechanism.
For many valuation spaces computing the allocation and payments of the VCG
mechanism, however, is a computationally hard problem. We thus study the
performance of the VCG mechanism when bidders are forced to choose bids from a
subspace of the valuation space for which the VCG outcome can be computed
efficiently. We prove improved upper bounds on the welfare loss for
restrictions to additive bids and upper and lower bounds for restrictions to
non-additive bids. These bounds show that the welfare loss increases in
expressiveness. All our bounds apply to equilibrium concepts that can be
computed in polynomial time as well as to learning outcomes
Expressiveness and Robustness of First-Price Position Auctions
Since economic mechanisms are often applied to very different instances of
the same problem, it is desirable to identify mechanisms that work well in a
wide range of circumstances. We pursue this goal for a position auction setting
and specifically seek mechanisms that guarantee good outcomes under both
complete and incomplete information. A variant of the generalized first-price
mechanism with multi-dimensional bids turns out to be the only standard
mechanism able to achieve this goal, even when types are one-dimensional. The
fact that expressiveness beyond the type space is both necessary and sufficient
for this kind of robustness provides an interesting counterpoint to previous
work on position auctions that has highlighted the benefits of simplicity. From
a technical perspective our results are interesting because they establish
equilibrium existence for a multi-dimensional bid space, where standard
techniques break down. The structure of the equilibrium bids moreover provides
an intuitive explanation for why first-price payments may be able to support
equilibria in a wider range of circumstances than second-price payments
Near-optimal asymmetric binary matrix partitions
We study the asymmetric binary matrix partition problem that was recently
introduced by Alon et al. (WINE 2013) to model the impact of asymmetric
information on the revenue of the seller in take-it-or-leave-it sales.
Instances of the problem consist of an binary matrix and a
probability distribution over its columns. A partition scheme
consists of a partition for each row of . The partition acts
as a smoothing operator on row that distributes the expected value of each
partition subset proportionally to all its entries. Given a scheme that
induces a smooth matrix , the partition value is the expected maximum
column entry of . The objective is to find a partition scheme such that
the resulting partition value is maximized. We present a -approximation
algorithm for the case where the probability distribution is uniform and a
-approximation algorithm for non-uniform distributions, significantly
improving results of Alon et al. Although our first algorithm is combinatorial
(and very simple), the analysis is based on linear programming and duality
arguments. In our second result we exploit a nice relation of the problem to
submodular welfare maximization.Comment: 17 page
The Economics of Internet Markets
The internet has facilitated the creation of new markets characterized by large scale, increased customization, rapid innovation and the collection and use of detailed consumer and market data. I describe these changes and some of the economic theory that has been useful for thinking about online advertising markets, retail and business-to-business e-commerce, internet job matching and financial exchanges, and other internet platforms. I also discuss the empirical evidence on competition and consumer behavior in internet markets and some directions for future research.internet, market, innovation, advertising, retail, e-commerce, financial exchanges
Constrained Signaling in Auction Design
We consider the problem of an auctioneer who faces the task of selling a good
(drawn from a known distribution) to a set of buyers, when the auctioneer does
not have the capacity to describe to the buyers the exact identity of the good
that he is selling. Instead, he must come up with a constrained signalling
scheme: a (non injective) mapping from goods to signals, that satisfies the
constraints of his setting. For example, the auctioneer may be able to
communicate only a bounded length message for each good, or he might be legally
constrained in how he can advertise the item being sold. Each candidate
signaling scheme induces an incomplete-information game among the buyers, and
the goal of the auctioneer is to choose the signaling scheme and accompanying
auction format that optimizes welfare. In this paper, we use techniques from
submodular function maximization and no-regret learning to give algorithms for
computing constrained signaling schemes for a variety of constrained signaling
problems
Simplicity-Expressiveness Tradeoffs in Mechanism Design
A fundamental result in mechanism design theory, the so-called revelation
principle, asserts that for many questions concerning the existence of
mechanisms with a given outcome one can restrict attention to truthful direct
revelation-mechanisms. In practice, however, many mechanism use a restricted
message space. This motivates the study of the tradeoffs involved in choosing
simplified mechanisms, which can sometimes bring benefits in precluding bad or
promoting good equilibria, and other times impose costs on welfare and revenue.
We study the simplicity-expressiveness tradeoff in two representative settings,
sponsored search auctions and combinatorial auctions, each being a canonical
example for complete information and incomplete information analysis,
respectively. We observe that the amount of information available to the agents
plays an important role for the tradeoff between simplicity and expressiveness
Near-optimal Asymmetric Binary Matrix Partitions
We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in take-it-or-leave-it sales. Instances of the problem consist of an binary matrix and a probability distribution over its columns. A partition scheme consists of a partition for each row of . The partition acts as a smoothing operator on row that distributes the expected value of each partition subset proportionally to all its entries. Given a scheme that induces a smooth matrix , the partition value is the expected maximum column entry of . The objective is to find a partition scheme such that the resulting partition value is maximized. We present a -approximation algorithm for the case where the probability distribution is uniform and a -approximation algorithm for non-uniform distributions, significantly improving results of Alon et al. Although our first algorithm is combinatorial (and very simple), the analysis is based on linear programming and duality arguments. In our second result we exploit a nice relation of the problem to submodular welfare maximization
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Expressiveness And Robustness of First-Price Position Auctions
Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments.Engineering and Applied Science