Transcript The New Economy – What is different with digital products

The New Economy –
auctions as mechanism and
content for the Web
Rudolf Müller
International Institute of Infonomics
[email protected]
Joint work with
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Stan van Hoesel, University Maastricht
Jan Hansen, HU Berlin
Carsten Schmidt, HU Berlin
Martin Strobel, HU Berlin
Outline
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About Infonomics
Auctions - mechanism and content
Auctions as a mechanism
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Auctions as content
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Internet auctions
Multi-item auctions
event markets
Summary
New science of Infonomics
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analyses the impact of digitization of
information on:
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individual and collective behavior
learning, cognitive patterns and competence
development
organizational and economic structure and
performance
ethical norms and values and the legal system
knowledge accumulation and diffusion
communication modes, democracy, culture
International
Institute of Infonomics
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Interdisciplinary research institute
Director Luc Soete
Research tracks
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e-basics (Paul Windrum, Rishab Ghosh)
e-behavior (Rita Walczuch)
e-organization (Rudolf Müller)
e-society (Huub Meijers)
e-content (Jan Bierhoff)
Auctions -
Mechanism and Content
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E-commerce changes traditional
mechanisms
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lower transaction costs
more interactivity, more knowledge
new intermediaries
Auctions are a good example
Auctions Mechanism and Content
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E-commerce invents new content
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totally digital products and services
almost zero cost for additional copy
high network externalities
Auctions are a good example
Some literature
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Miriam Herschlag and Rami Zwick
Internet Auctions - Popular and Professional
Literature Review, WWW (1999)
Agorics, Inc. Auctions. Going, Going, Gone! A Survey
of Auction Types, WWW (2000)
Sven de Vries and Rakesh Vohra, Combinatorial
Auctions: A Survey, from the authors (2000)
Rudolf Müller and Stan van Hoesel, Optimization in
Electronic Markets - Examples from Combinatorial
Auctions, Netnomics (2000)
Auctions Mechanism
Four standard formats
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open, increasing bid:
English auction
open, decreasing bid:
Dutch auction
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closed, second price:
Vickrey Auction
closed, highest price:
discriminating auction
Internet Auctions
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Private to private auctions
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Business to consumer
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successful format
customer satisfaction is a problem
popular live auctions
Business to business
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in particular for perishable goods
format: multi-item
Multi-item auctions
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Bidders observe (dis-)economies of scale:
valuation of a set of assets is smaller or
larger than the sum of the valuations
Problems if assets are auctioned
independently: threshold problem, exposure
problem, efficiency, optimality
Widely discussed in the context of frequency
auctions
Example instance
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3 assets P,Q,R
sequential English auction
5 bidders
private valuation
every bidder wants to purchase at
most one asset
Private valuations
P
Q R
A
10 6
9
B
8
5
4
C
7
3
3
D 6
3
2
E
2
4
3
Nobody has information
P
Q
R
A
8+2
B
8
3+2
C
7
3
3
D 6
3
2
E
2
3+1
3
Winning bid
Profit
A knows valuations of B - E
P
Q
A
10-5 6-5
B
7+1
C
7
R
4+5
3+0
D 6
3
2
E
2
4
3
Reduced willingness
to pay
All have information about
others valuations
P
Q
A
10-5 6-5
B
8-2
C
6+1
R
4+5
3+2
D 6
3
2
E
2
4
3
General case
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bidders have knowledge about distribution
of other bidders valuation
bidders bid less in order to maximize
expected return
costs for getting information reduce the
expected profit
Vickrey-Clarke-Groves
auction scheme
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Every bidder x makes sealed bid p(x,s) for
every asset s
Auctioneer computes assignment with
maximum revenue zmax
Price p*(x,s) to pay for bidder x for
winning bid s:
p*(x,s) = p(x,s) - (zmax - zmax(without x))
= zmax(without x) - (zmax - p(x,s))
Result in our example
Assume: A, B, C, D, E bid their valuation
PP Q
RR
Q R
Q
AA 10
10 666 99 4(5)
B
B 88 553(2)44 4
C 7
6(1) 33 33 3
D
D 66 333 22 2
E
EE 333 222 44 4
Winner: C(P), B(Q), A(R)
Price that C has to pay:
Rev. without C
20
- Revenue from
other bids
-14
To pay
6
Comparison of results
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The Vickrey-Clarke-Groves design
results in the same assignment at the
same prices without
requiring bidders to invest in getting
information.
But: Will all bidders reveal true
valuation?
Valuation revealing
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Theorem (Clarke 1971, Groves 1973)
Revealing true valuation is a dominant
strategy
But: how are the winning bids and their
prices computed by the auctioneer?
Computation in our example:
Bipartite Matching
A
B
10
C
6
P
Q
Rothkopf, Pekeč, Harstad (1998)
D
9
E
R
Algorithmic questions for
combinatorial bids
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Does there exist a polynomial time
algorithm to solve the winner
assignment, or is the problem NP-hard?
If it is NP-hard, does additional
structure make it polynomial solvable?
If it is hard, can a smart algorithm solve
the problem in reasonable time?
3-dim matching is a
combinatiorial auction
Left nodes are the bidders, they bid 1 $ on grey and
blue nodes covered by the triangles. How many
bids can be assigned to bidders?
Identical Assets:
polynomial solvable
Every bidder bids on numbers of assets:
bij price by bidder i for j assets.
Let m(i,s) be the value of the optimal
assignment if bids by bidders 1,…,i are
considered and at most s assets are assigned.
m(1, s)  max(b1 j | j  s)
m(i  1, s)  max(bi  1, j  m(i, s  j ) | j  s)
Linearly ordered assets
Bidders bid on sets of neighboured assets
Polynomial solvable if we allow to assign
more than one bid per bidder (Rothkopf et al.)
Complexity unknown, if we allow to assign at
most one bid to every bidder.
Integer linear programming
test results
bidders
10
20
30
40
size
linear
random
assets bids
time
nodes time nodes
30
150
0
3 0,07
605
40
300
0
0 0,27
1811
50
450
0
0 2,16
5508
60
600
0
0 11,2
20200
Linear instances are much easier to solve.
Medium sized random instances are solvable.
Related Research
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Gomber, Schmidt, Weinhardt, Efficiency, incentives
and computational tractability in MAS-Coordination
Rothkopf, Pekec, Harstad, Computationally
manageable combinational auctions
Sandholm, An algorithm for optimal winner
determination in combinatorial auctions
Andersson, Tenhune, Ygge, Integer Programming for
Combinatorial Auction Winner Determination
Fujishima, Leyton-Brown and Shohan, Taming the
computational complexity of combinatorial auctions
Auctions as content:
Trading event bets
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Customers buy and sell shares that
represent events in a virtual stock
market
Final price depends on outcome of
event
Example: election markets in the US.
Final price = percentage of a political
party at the election
Example: EURO 2000 market
www.voetbalmarkt.nl
www.fussballmarkt.de
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Example event: England – Germany
Three types of shares: E wins, G wins, draw
Value after the game: 1000 if event true
Participants buy bundles at price 1000 with
one share of each team
Use the market to trade individual shares
Note: market prices predict the outcome of
the event
A double auction - interface
of the EURO 2000 market
Information processing in
event markets
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A stock market is able to translate
information of traders into market
prices
Applications:
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Auctions on events inside a company:
when will a project be completed?
Auctions on new products: what market
share can a product gain?
Research questions
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How efficient is information translated
(in election markets small parties are
overpriced)?
How does the market influence the
opinion of a trader?
Is it legal to do such auctions via the
Internet?
Summary
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Auctions provide mechanisms and
content in the New Economy
Auction mechanisms challenge game
theory, operations research and
experimental economics
Event trading provides content and
testbed for experimental economics
Integer linear programming
x i,j = 1 if bidder i is assigned set Sij, 0 else.
max  bijxij
i, j
k  S : 
x
ij
iB j:kSij
i  B :  xij  1
i, j : xij  {0,1}
1
Complexity: Node packing is
a combinatorial auction
Every node is willing to pay 1 $ for its adjacent
edges. How many nodes can be assigned a bid?