3,726 research outputs found
Information disclosure by a seller in sequential first-price auctions
I study sequential first-price auctions where two items are sold to two bidders with private binary valuations. A seller, prior to the second auction, can publicly disclose some information about the outcome of the first auction. I characterize equilibrium strategies for various disclosure rules when the valuations of bidders are either perfectly positively or perfectly negatively correlated across items. I establish outcome equivalence between different disclosure rules. I find that it is optimal for the seller to disclose some information when the valuations are negatively correlated, whereas it is optimal not to disclose any information when the valuations are positively correlated. For most of the parameter values, the seller’s expected revenue is higher if the losing bid is disclosed. When only the winner’s identity is disclosed, the equilibrium is efficient whether the valuations are positively or negatively correlated
On Simultaneous Two-player Combinatorial Auctions
We consider the following communication problem: Alice and Bob each have some
valuation functions and over subsets of items,
and their goal is to partition the items into in a way that
maximizes the welfare, . We study both the allocation
problem, which asks for a welfare-maximizing partition and the decision
problem, which asks whether or not there exists a partition guaranteeing
certain welfare, for binary XOS valuations. For interactive protocols with
communication, a tight 3/4-approximation is known for both
[Fei06,DS06].
For interactive protocols, the allocation problem is provably harder than the
decision problem: any solution to the allocation problem implies a solution to
the decision problem with one additional round and additional bits of
communication via a trivial reduction. Surprisingly, the allocation problem is
provably easier for simultaneous protocols. Specifically, we show:
1) There exists a simultaneous, randomized protocol with polynomial
communication that selects a partition whose expected welfare is at least
of the optimum. This matches the guarantee of the best interactive, randomized
protocol with polynomial communication.
2) For all , any simultaneous, randomized protocol that
decides whether the welfare of the optimal partition is or correctly with probability requires
exponential communication. This provides a separation between the attainable
approximation guarantees via interactive () versus simultaneous () protocols with polynomial communication.
In other words, this trivial reduction from decision to allocation problems
provably requires the extra round of communication
Seller Strategies on eBay
This paper analyzes seller characteristics and choices in approximately 1000 eBay auctions for a particular model of PDA. Seller characteristics include frequency of selling, reputation, and the qualities of the product sold. Seller choices include the length of the auction, information provided about the product, starting price, and whether to use a ‘Buy it Now’ option. We find that different types of sellers pursue systematically different strategies for how their items are offered, and we discuss the possible causes of these differences. For example, the two high volume sellers in our sample always use a combination of a ‘Buy it Now’ with a low starting price, while the many less frequent sellers use an array of pricing strategies. In addition, more highly rated sellers were somewhat more likely to provide more detailed product information, as well as secure payment options.
Combinatorial Auctions Do Need Modest Interaction
We study the necessity of interaction for obtaining efficient allocations in
subadditive combinatorial auctions. This problem was originally introduced by
Dobzinski, Nisan, and Oren (STOC'14) as the following simple market scenario:
items are to be allocated among bidders in a distributed setting where
bidders valuations are private and hence communication is needed to obtain an
efficient allocation. The communication happens in rounds: in each round, each
bidder, simultaneously with others, broadcasts a message to all parties
involved and the central planner computes an allocation solely based on the
communicated messages. Dobzinski et.al. showed that no non-interactive
(-round) protocol with polynomial communication (in the number of items and
bidders) can achieve approximation ratio better than ,
while for any , there exists -round protocols that achieve
approximation with polynomial
communication; in particular, rounds of interaction suffice to
obtain an (almost) efficient allocation.
A natural question at this point is to identify the "right" level of
interaction (i.e., number of rounds) necessary to obtain an efficient
allocation. In this paper, we resolve this question by providing an almost
tight round-approximation tradeoff for this problem: we show that for any , any -round protocol that uses polynomial communication can only
approximate the social welfare up to a factor of . This in particular implies that
rounds of interaction are necessary for
obtaining any efficient allocation in these markets. Our work builds on the
recent multi-party round-elimination technique of Alon, Nisan, Raz, and
Weinstein (FOCS'15) and settles an open question posed by Dobzinski et.al. and
Alon et. al
Seller strategies on eBay: Does size matter?
We examine seller strategies in 1177 Internet auctions on eBay, to understand the diversity of strategies used, and their impacts. Dimensions of strategic choice include the use of a ‘Buy it Now’ option, the level of the starting price, and the use of a secret reserve price. A major focus of our analysis is on differences across sellers with different volumes of sales. The largest volume sellers (termed “retailers”) in our sample employ uniform selling strategies, but lower volume sellers exhibit a wide variety of strategic choices. While some components of sellers’ strategies appear important in raising seller revenue, including starting the auction with a ‘Buy it Now’ offer, the overall impact of seller strategy choices on the outcome appears to be quite small. We interpret this as evidence for the competitiveness of the online auction market for frequently traded items with conventional retail alternatives. An exception is provided by the use of a secret reserve price, which raises the winning bid conditional on a sale, but reduces the probability of a sale. Depending on sellers’ risk aversion and impatience, this may also be an efficient outcome
Third-Party Data Providers Ruin Simple Mechanisms
Motivated by the growing prominence of third-party data providers in online
marketplaces, this paper studies the impact of the presence of third-party data
providers on mechanism design. When no data provider is present, it has been
shown that simple mechanisms are "good enough" -- they can achieve a constant
fraction of the revenue of optimal mechanisms. The results in this paper
demonstrate that this is no longer true in the presence of a third-party data
provider who can provide the bidder with a signal that is correlated with the
item type. Specifically, even with a single seller, a single bidder, and a
single item of uncertain type for sale, the strategies of pricing each
item-type separately (the analog of item pricing for multi-item auctions) and
bundling all item-types under a single price (the analog of grand bundling) can
both simultaneously be a logarithmic factor worse than the optimal revenue.
Further, in the presence of a data provider, item-type partitioning
mechanisms---a more general class of mechanisms which divide item-types into
disjoint groups and offer prices for each group---still cannot achieve within a
factor of the optimal revenue. Thus, our results highlight that the
presence of a data-provider forces the use of more complicated mechanisms in
order to achieve a constant fraction of the optimal revenue
Prophet Inequalities with Limited Information
In the classical prophet inequality, a gambler observes a sequence of
stochastic rewards and must decide, for each reward ,
whether to keep it and stop the game or to forfeit the reward forever and
reveal the next value . The gambler's goal is to obtain a constant
fraction of the expected reward that the optimal offline algorithm would get.
Recently, prophet inequalities have been generalized to settings where the
gambler can choose items, and, more generally, where he can choose any
independent set in a matroid. However, all the existing algorithms require the
gambler to know the distribution from which the rewards are
drawn.
The assumption that the gambler knows the distribution from which
are drawn is very strong. Instead, we work with the much simpler
assumption that the gambler only knows a few samples from this distribution. We
construct the first single-sample prophet inequalities for many settings of
interest, whose guarantees all match the best possible asymptotically,
\emph{even with full knowledge of the distribution}. Specifically, we provide a
novel single-sample algorithm when the gambler can choose any elements
whose analysis is based on random walks with limited correlation. In addition,
we provide a black-box method for converting specific types of solutions to the
related \emph{secretary problem} to single-sample prophet inequalities, and
apply it to several existing algorithms. Finally, we provide a constant-sample
prophet inequality for constant-degree bipartite matchings.
We apply these results to design the first posted-price and multi-dimensional
auction mechanisms with limited information in settings with asymmetric
bidders
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