747 research outputs found
On the Inefficiency of the Uniform Price Auction
We present our results on Uniform Price Auctions, one of the standard
sealed-bid multi-unit auction formats, for selling multiple identical units of
a single good to multi-demand bidders. Contrary to the truthful and
economically efficient multi-unit Vickrey auction, the Uniform Price Auction
encourages strategic bidding and is socially inefficient in general. The
uniform pricing rule is, however, widely popular by its appeal to the natural
anticipation, that identical items should be identically priced. In this work
we study equilibria of the Uniform Price Auction for bidders with (symmetric)
submodular valuation functions, over the number of units that they win. We
investigate pure Nash equilibria of the auction in undominated strategies; we
produce a characterization of these equilibria that allows us to prove that a
fraction 1-1/e of the optimum social welfare is always recovered in undominated
pure Nash equilibrium -- and this bound is essentially tight. Subsequently, we
study the auction under the incomplete information setting and prove a bound of
4-2/k on the economic inefficiency of (mixed) Bayes Nash equilibria that are
supported by undominated strategies.Comment: Additions and Improvements upon SAGT 2012 results (and minor
corrections on the previous version
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
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
Generalized Second Price Auction with Probabilistic Broad Match
Generalized Second Price (GSP) auctions are widely used by search engines
today to sell their ad slots. Most search engines have supported broad match
between queries and bid keywords when executing GSP auctions, however, it has
been revealed that GSP auction with the standard broad-match mechanism they are
currently using (denoted as SBM-GSP) has several theoretical drawbacks (e.g.,
its theoretical properties are known only for the single-slot case and
full-information setting, and even in this simple setting, the corresponding
worst-case social welfare can be rather bad). To address this issue, we propose
a novel broad-match mechanism, which we call the Probabilistic Broad-Match
(PBM) mechanism. Different from SBM that puts together the ads bidding on all
the keywords matched to a given query for the GSP auction, the GSP with PBM
(denoted as PBM-GSP) randomly samples a keyword according to a predefined
probability distribution and only runs the GSP auction for the ads bidding on
this sampled keyword. We perform a comprehensive study on the theoretical
properties of the PBM-GSP. Specifically, we study its social welfare in the
worst equilibrium, in both full-information and Bayesian settings. The results
show that PBM-GSP can generate larger welfare than SBM-GSP under mild
conditions. Furthermore, we also study the revenue guarantee for PBM-GSP in
Bayesian setting. To the best of our knowledge, this is the first work on
broad-match mechanisms for GSP that goes beyond the single-slot case and the
full-information setting
Draft Auctions
We introduce draft auctions, which is a sequential auction format where at
each iteration players bid for the right to buy items at a fixed price. We show
that draft auctions offer an exponential improvement in social welfare at
equilibrium over sequential item auctions where predetermined items are
auctioned at each time step. Specifically, we show that for any subadditive
valuation the social welfare at equilibrium is an -approximation
to the optimal social welfare, where is the number of items. We also
provide tighter approximation results for several subclasses. Our welfare
guarantees hold for Bayes-Nash equilibria and for no-regret learning outcomes,
via the smooth-mechanism framework. Of independent interest, our techniques
show that in a combinatorial auction setting, efficiency guarantees of a
mechanism via smoothness for a very restricted class of cardinality valuations,
extend with a small degradation, to subadditive valuations, the largest
complement-free class of valuations. Variants of draft auctions have been used
in practice and have been experimentally shown to outperform other auctions.
Our results provide a theoretical justification
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