Talk
Abstracts:
Material
from Talks
G.
Anandalingam (Systems Engineering and The Wharton
School University of Pennsylvania Philadelphia PA) and Neil
J. Keon (Edwin L. Cox School of Business Southern
Methodist University)
Pricing
of Multiple Services in Telecommunications Networks With Quality
of Service Guarantees
We
consider pricing of multiple services offered over a single
telecommunications network. Each service has quality of service
(QoS) requirements that are guaranteed to users. Service classes
may be defined by the type of service, such as voice, video
or data, as well as the origin and destination of the connection
provided to the user. We formulate the optimal pricing problem
as a mathematical program. We solve for both prices and resource
allocations necessary to provide connections with guaranteed
QoS, to serve the demand resulting from the prices. We derive
optimality conditions and a solution method for this class of
problems.
John
R. Birge (Dean, McCormick School of Engineering and
Applied Science, Northwestern University) jrbirge@northwestern.edu
Equilibria
in Electric Power Exchange Auction Markets
Deregulated
electric power markets have been increasingly transformed into
auction clearing houses. We will describe the structure of these
markets and the forms of equilibria that can exist. We will
give characterizations of equilibria in simple stylized markets
and illustrate conditions that produce apparent paradoxes such
as declining prices during periods of high demand. We will also
discuss some experience with the market in Colombia and the
difficulties in using pure optimization procedures in predicting
auction behavior or devising bidding strategies.
Brenda
Dietrich (IBM T.J. Watson Research Center) and
John Forrest
Column
Generation Methods for Combinatorial Auctions
This paper discusses model formulations for solving combinatorial
auctions using column generation techniques. We include the
details of a solver developed for the FCC spectrum auction,
formulations of other combinatorial auctions, and preliminary
computational experience based on sample data for the FCC auction.
Brenda
Dietrich
(IBM T.J. Watson Research
Center) and Jayant Kalagnanam
Examples
of Complex Marketplaces: Customers, Models and Solution Methods
We
discuss three classes of complex marketplaces: direct procurement,
indivisible supply/demand, and combinatorial bids with type
constraints. For each, we describe the commerce environment,
the mathematical models and the solution methods.
In weekly direct procurement, suppliers submit bundled bids
for multiple commodities. The goal is to select a minimum ocst
set of bids that meet all requirements while satisfying additional
constraints such as a minimum number of suppliers for each commodity
and maximum number os suppliers.
Certain commodities such as steel and paper need to be sourced
from a single supplier; a bid for a 2 feet wide galvanized coil
cannot be satisfied by two 1 foot wide coils. The introduction
of such indivisability constraints makes the problem of finding
the set of winning bids and asks NP-hard and can be modeled
as a generalized assignment problem.
Based on a liability limiting constraint proposed by the FCC
for its license auction, we formulate a more general type-based
bidding system for combinatorial auctions, and discuss a column
generation approach for solving such auctions.
Suzhou Huang (Ford
Motor Company)
Pricebot
Dynamics
We
study a class of dynamic pricing duopoly games that model the
type of environment in which e-commerce will be carried out
in not so distant future. Under Markov settings these games
can be solved via backward induction. The equilibrium structure
is found to display very complex patterns when parameters of
the model are varied, due to bifurcation phenomena in the discrete
map induced by backward induction. However, it is possible to
define an effective but simpler dynamics that retains the optimality
of the original game in the long run. We further show that this
effective dynamics can be sustained by steady self-confirming
equilibria. Our results (1) set limits on what learning algorithms
based on Markov assumptions can obtain and (2) imply that learning
in this kind of games should not be focused on the exact reaction
functions, but rather on achieving optimal net present values
with the realized time series of prices.
Jeffrey
O. Kephart (Institute for Advanced Commerce IBM Thomas
J. Watson Research Center) kephart@us.ibm.com
Dynamic
Pricing by Software Agents
We
envision a future in which the world economy and the Internet
will merge and evolve into an information economy bustling with
billions of economically motivated software agents that exchange
information goods and services with humans and other agents.
These software agents will constitute a new economic species
that differs in some significant ways from humans. What impact
might collective interactions among agents have on market behavior,
and on the global economy as a whole?
In
this talk, I will focus on collective interactions among software
agents that dynamically price information goods or services.
I will discuss two types of dynamic pricing. First, I will cover
a few examples of dynamic posted pricing, in which automated
pricing agents ("pricebots") continually adjust the price of
a commodity (or the price and attributes of a more complex product)
in an effort to maximize profits. The price dynamics that result
from interactions among pricebots are often quite complex, sometimes
to the detriment of buyers as well as sellers. I will describe
the connection of these and other nonlinear dynamical effects
to optimization and learning. Second, I will discuss some very
recent work on bidding algorithms for agents. We have found
that relatively simple algorithms for a multi-unit continuous
double auction consistently outperform humans in controlled
experiments involving students and IBM Researchers.
John
Ledyard (California Institute of Technology)
Optimal
Mechanism Design for Internet Auctions
Paul
Milgrom (Stanford University)
Putting
Auction Theory to Work: Ascending Auctions with Package Bidding
After
reviewing the factors contributing to the present interest in
new package bidding designs, a benchmark ascending auction with
package bidding is described. If bidders bid straightforwardly
at each round for the potentially most profitable package, the
allocation converges to an approximately efficient one. Straightforward
bidding is consistent with equilibrium when there are only two
bidders and it is a best reply to straightforward bidding by
other bidders for a bidder that wants to acquire all the items
for sale. More generally, if others bid straightforwardly, then
non-monotonicity in the prices over time create an incentive
for bidders to delay making serious bids, increasing the time
requirements and degrading the performance of the auction.
Alvin
E. Roth
(Harvard University) and Axel Ockenfels
Last
Minute Bidding and the Rules for Ending Second Price Auctions:
Theory and Evidence from a Natural Experiment on the Internet
An important issue in auction design concerns the rules governing
the end of the auction. The internet auctions conducted by eBay
and Amazon present a natural experiment because they use different
rules for ending an auction. Auctions on eBay have a fixed end
time, while auctions on Amazon, which operate under otherwise
similar rules, do not have a fixed end time, but continue if
necessary past the scheduled end time until ten minutes have
passed without a bid. The strategic differences in the auction
rules are reflected in the auction data by significantly more
late bidding on eBay than on Amazon. Furthermore, more experienced
bidders on eBay submit late bids more often than do less experienced
bidders, while the effect of experience on Amazon goes in the
opposite direction. On eBay, there is also more late bidding
for antiques than for computers. We also find scale independence
in the distribution over time of bidders' last bids, of a form
strikingly similar to the 'deadline effect' noted in bargaining:
last bids are distributed according to a power law. Both the
theory and the data suggest that multiple causes contribute
to late bidding, with strategic issues related to the rules
about ending the auction playing an important role.
Michael
H. Rothkopf (RUTCOR and Faculty of Management, Rutgers
University) Rothkopf@rutcor.rutgers.edu
Modeling
Opportunities in Auctions
This paper argues that the answers to interesting questions
about real auctions depend, often critically, on the particular
mathematical assumptions that go into a model of an auction
situation. It then suggests some understudied areas for fruitful
mathematical research on competitive bidding. These include
asymmetry, financially constrained bidders, complicated information
structures, bidder decisions about auction participation, the
effect of repeated auctions involving the same participants,
auctioning items with interrelated values, and transaction costs.
The paper also discusses two major areas where new, complicated
auctions are being designed: combinatorial spectrum auctions
and electricity and transmission rights auctions.
Garrett
van Ryzin
(Columbia University, Graduate School of Business)
Airline
Revenue Management and e-Markets
Revenue (or yield) management uses applied mathematical methods
to intelligently control the availability of price discounts.
While the practice in airlines predates the internet by several
decades, it shares some common features with dynamic pricing
in e-markets. Moreover, airline tickets are among the highest
volume consumer products sold through new e-commerce pricing
mechanisms. Thus, a convergence of these two developments appears
to be well underway. In this talk, we discuss the traditional
revenue management problem and survey the mathematical models
and algorithms that have been developed in this area. We then
examine the impact of e-market innovations such as Priceline.com?s
guaranteed purchase contracts, ticket auctions, etc. on the
practice of revenue management. While some have suggested that
auctions and similar innovations will completely replace traditional
price mechanisms, a melding of new and old looks more likely.
We discuss the research challenges that arise from this integration.
Rakesh
V. Vohra (Northwestern
University)
Combinatorial
Auctions: A Survey
(Joint with Sven de Vries).
As the title suggests, its a survey. I will focus on the interplay
between Integer Programming and Auction design.
Robert Weber
(Northwestern University)
(Public
Lecture, Monday night)
The Other
Side of the (e-Commerce) Fence
Economic markets occasionally fail to work as intended. Sometimes
the problem is less-than-rational behavior on the part of market
participants. At other times participants, individually or collectively,
are more rational than the market organizers anticipate, and,
legally or otherwise, find ways to subvert a market to their
own ends. Those seeking to build e-commerce marketplaces must
take care to look at their systems through the eyes of those
who will be players in the market.
Material
from Talks
IMA
"HOT TOPICS" Workshop: Mathematics of the Internet: E-Auction
and Markets
"Hot
Topics" Workshops
2000-2001
Program: Mathematics in Multimedia
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