3,787 research outputs found
Optimal complementary auctions
This paper considers the situation where two products are sold by the same seller, but to disjoint sets of potential buyers. Externalities may arise from each market outcome to the other. The paper examines the nature of the seller's optimal mechanism, and, for example in the case of positive externalities, it is shown that the allocation decision in either market depends on the highest types in both markets. The optimal mechanism can be implemented by an indirect mechanism that essentially charges winning bidders for the value of their externalities. The analysis is applied to the sale of public sector franchises including exploration and development rights for oil and gas tracts
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
Aversion to price risk and the afternoon effect
Many empirical studies of auctions show that prices of identical goods sold sequentially follow a declining path. Declining prices have been viewed as an anomaly, because the theoretical models of auctions predict that the price sequence should either be a martingale (with independent signals and no
informational externalities), or a submartingale (with affiliated signals). This paper shows that declining prices, the afternoon effect, arise naturally when bidders are averse to price risk. A bidder is averse to price risk if he prefers to win an object at a certain price, rather than at a random price with the same expected value. When bidders have independent signals and there are no informational externalities, only the effect of aversion to price risk is present and the price sequence is a supermartingale. When there are informational externalities, even with independent signals, there is a countervailing, informational effect, which pushes prices to raise along the path of a sequential auction. This may help explaining the more complex price paths we observe in some auctions
Sequential item pricing for unlimited supply
We investigate the extent to which price updates can increase the revenue of
a seller with little prior information on demand. We study prior-free revenue
maximization for a seller with unlimited supply of n item types facing m myopic
buyers present for k < log n days. For the static (k = 1) case, Balcan et al.
[2] show that one random item price (the same on each item) yields revenue
within a \Theta(log m + log n) factor of optimum and this factor is tight. We
define the hereditary maximizers property of buyer valuations (satisfied by any
multi-unit or gross substitutes valuation) that is sufficient for a significant
improvement of the approximation factor in the dynamic (k > 1) setting. Our
main result is a non-increasing, randomized, schedule of k equal item prices
with expected revenue within a O((log m + log n) / k) factor of optimum for
private valuations with hereditary maximizers. This factor is almost tight: we
show that any pricing scheme over k days has a revenue approximation factor of
at least (log m + log n) / (3k). We obtain analogous matching lower and upper
bounds of \Theta((log n) / k) if all valuations have the same maximum. We
expect our upper bound technique to be of broader interest; for example, it can
significantly improve the result of Akhlaghpour et al. [1]. We also initiate
the study of revenue maximization given allocative externalities (i.e.
influences) between buyers with combinatorial valuations. We provide a rather
general model of positive influence of others' ownership of items on a buyer's
valuation. For affine, submodular externalities and valuations with hereditary
maximizers we present an influence-and-exploit (Hartline et al. [13]) marketing
strategy based on our algorithm for private valuations. This strategy preserves
our approximation factor, despite an affine increase (due to externalities) in
the optimum revenue.Comment: 18 pages, 1 figur
How to sell to buyers with crossholdings
This paper characterizes the optimal selling mechanism in the presence of horizontal
crossholdings. We find that this mechanism imposes a discrimination policy against the
stronger bidders so that the sellerÂŽs expected revenue is increasing in both the
common crossholding and the degree of asymmetry in crossholdings. Furthermore, it
can be implemented by a sequential procedure that includes a price-preferences
scheme and the possibility of an exclusive deal with the weakest bidder. We also show
that a simple sequential negotiation mechanism, although suboptimal, yields a larger
sellerÂŽs expected revenue than both the first-price and the second-price auctions
Bidding among friends and enemies
We consider an auction setting in which bidders, even if they fail
to obtain the good, care about the price paid by the winner. We study
the impact of these price externalities on the first-price auction and
the second-price auction in a symmetric information framework. We
establish a distinction between price externalities that do not depend
on the identity of the winner and price externalities that depend on
the identity of the winner. We prove that the outcome of the first-price
auction is not affected by the first type of price externalities while the
outcome of the second-price auction is. In contrast, the second type
of price externalities affects the outcome of both auction formats. In
any case, in comparison with the first-price auction, the second-price
auction exacerbates the effects of price externalities whatever their
types are. The two auction formats are generically not equivalent
Optimal takeover contests with toeholds
This paper characterizes how a target firm should be sold when the possible buyers (bidders) have prior stakes in its ownership (toeholds). We find that the optimal mechanism needs to be implemented by a non-standard auction which imposes a bias against bidders with high toeholds. This discriminatory procedure is such that the targetÂŽs average sale price is increasing in both the size of the common toehold and the degree of asymmetry in these stakes. It is also shown that a simple mechanism of sequential negotiation replicates the main properties of the optimal procedure and yields a higher average selling price than the standard auctions commonly used in takeover battles.Optimal auctions, Takeovers, Toeholds, Asymmetric auctions
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