Abstracts and earlier versions of published papers:
·
“Favoritism in
Asymmetric Contests: Head Starts and Handicaps”, Games and Economic Behavior, forthcoming.
Abstract: I examine a contest with identity-dependent rules in which contestants
are privately informed and ex ante heterogenous. A
contestant may suffer from a handicap or benefit from a head start. The former
reduces the contestant's score by a fixed percentage; the latter is an additive
bonus. Although total effort increases if the weak contestant is favored with a
head start, the optimal use of handicaps is not as clear-cut. Depending on the
nature of the asymmetry, it may or may not be optimal to handicap the strong
contestant. Moreover, it is generally optimal to combine the two instruments.
For instance, when contestants are sufficiently heterogenous
the weak contestant should be given both a head start and a handicap. It may
also be possible to induce higher effort and at the same time make both
contestants better off ex ante. [paper]
An earlier version with a more detailed analysis of bidders’
payoffs is here: [WP version]
Abstract: I propose a new mechanism
design approach to the problem of ranking standard auctions with two
heterogeneous bidders. A key feature of the approach is that it may be possible
to rank two auctions even if neither dominates the other for all combinations
of types. The approach simplifies the analysis and unifies results in the
existing literature. Roughly speaking, the first-price auction is more
profitable than the second-price auction when the strong bidder's distribution
is flatter and more disperse than the weak bidder's distribution. Applications
include auctions with one-sided externalities. Moreover, contrary to previous
work, reserve prices are easily handled. Finally, the method can be extended to
some environments with many bidders. [paper] [online
appendix]
The paper is
based on (and extends) parts of “Ranking Asymmetric Auctions using the
Dispersive Order”. [paper]
Abstract: A new approach to asymmetric first price auctions is proposed which
circumvents the need to examine bidding strategies directly. Specifically, the
ratio of bidders' (endogenous) payoffs is analyzed and compared to the ratio of
the (exogenous) distribution functions that describe beliefs. Most of the
results are inferred from this comparison. In the existing theoretical
literature, assumptions of first order stochastic dominance or stronger imply
that the latter ratio has very specific properties, but no such assumptions are
imposed here. It is proven that first order stochastic dominance is necessary for
bidding strategies not to cross. When this assumption is relaxed in the
numerical literature it is done in a manner that leads to exactly one crossing.
However, it is straightforward to construct examples with several crossings.
Finally, the bid distributions (and strategies) will cross in auctions with two
bidders whenever second order stochastic dominance applies. [paper]
An earlier
version with more examples, discussion, etc. is available. [earlier
version]
Abstract: Online auction sites often enable
sellers to add a buy-out price. In one-shot auctions, this has been motivated
by appeal to impatience or risk aversion. We offer additional justification in
a dynamic model, by showing that an early seller has an incentive to use a
buy-out price, if a similar product is offered later by another seller, and
bidders desire multiple objects. Revenue in the first auction increases, but
revenue in the second auction decreases, as does the sum of revenues. The
buy-out price causes the auction sequence to become inefficient, since the
first item may be awarded to a bidder who should have received none. [paper] [appendix]
An earlier
version circulated under the title: “Buy-Out Prices in Online Auctions:
Multi-Unit Demand”. [paper]
Abstract: Comparative statics
for all-pay auctions with two heterogeneous and privately informed bidders are
analyzed. General results are provided for when one bidder becomes
stochastically weaker. The comparative statics are fully characterized for
truncations. Moreover, we show that expected revenue may increase when one
bidder weakens. In the second part of the paper we consider a dynamic contest
in which beliefs change endogenously: the first bidder may preempt the auction
by paying a bribe. An all-pay auction is held if the bribe is not paid, in
which case the second bidder revises his beliefs. With the option to bribe,
expected payoff decreases for a set of types of at least one bidder, possibly
the bidder ostensibly advantaged by the preemption option. However, the
expected revenue and the ex ante payoff of both bidders may improve. [paper]
Abstract: We consider first-price and
second-price auctions with asymmetric buyers, and examine whether pre-auction
offers to a subset of buyers are profitable. A single offer is never
profitable prior to a second-price auction, but may be profitable prior to a
first-price auction. However, a sequence of offers is profitable in
either type of auction. In our model, suitably chosen pre-auction offers work
because they move the assignment when bidder valuations are “near the
top” closer to the optimal, revenue-maximizing assignment. [paper]
Abstract: Bulow and Klemperer [1] have
provided an upper bound on the value of bargaining power for a seller of an
indivisible object. Specifically, negotiating optimally with N buyers
yields lower revenue than an English auction with N +1 buyers. In this paper, a short and intuitive proof of this
result is presented. [paper]
Abstract: In English auctions with weak and strong buyers, the equilibrium
revenue arising from using the optimal reserve price is shown to be higher than
the expected revenue in any “intuitive” equilibrium of an auction
with a participation fee. [paper]