Computational Mechanisms for Multi-Attribute Exchange Markets

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Computational Mechanisms for Multi-Attribute
Exchange Markets
Eugene Fink
Part I Research interests and projects Part II
Automated exchange system
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Part I Research Interests and Projects
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Research interests

• Artificial intelligence
• Machine learning

• Algorithm theory
• Computational geometry

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Research projects

• Artificial intelligence
• Machine learning

• Algorithm theory
• Computational geometry

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Representation changes Artificial intelligence
and learning
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Medical expert systems Artificial intelligence

• Guiding a nurse through the related questions
• Identifying the appropriate medical tests
• Reducing the cost of the selection process

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Approximate data matching Artificial
intelligence, learning, and algorithms

• Indexing of alphanumeric data
• Search for approximate matches
• Application to homeland security

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Indexing of time series Artificial intelligence
and algorithms
4

• Fast compression of time series

• Hierarchical indexing of compressed series

• Search for series similar to a given pattern

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Meshing in three dimensions Algorithms and
computational geometry

• Indexing in three dimensions
• Search for optimal meshes
• Repair of meshes with holes

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Generalized convexity Computational geometry
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Part II Automated Exchange System for
Multi-Attribute Markets
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Outline

• Motivation
• Main concepts
• Architecture
• Best-price matches
• Quality functions
• Performance
• Conclusions

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Motivation

• Build an automated
• exchange for trading
• goods and services

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Previous work

• Combinatorial auctions
• Standardized exchanges

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Combinatorial auctions

• Complex goods
• Asymmetry between
• buyers and sellers
• Illiquid

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Standardized exchanges

• Simple goods
• Symmetry between
• buyers and sellers
• Liquid

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Research goals
Build an automated exchangefor non-standardized
goods.

• Allow complex constraints in the
  specification of desirable trades

• Support fast-paced trading for markets with
  millions of orders

• Include optimization techniques to maximize
  traders satisfaction

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Outline

• Motivation
• Main concepts
• Architecture
• Best-price matches
• Quality functions
• Performance
• Conclusions

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Main concepts

• Market
• Orders
• Matches
• Fills
• Attributes

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Market
All items that can be traded form a market.
Example All conceivable vehicles compose a car
market.
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Orders
An order is a subset of the market along with a
price function.

Mustang for 28,000 or Corvette for 32,000
Example Any Mustang or Corvette
, 1 for
every ten miles.
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Orders
Price
Buy order
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Matching
A buy order matches a sell order if There is
item buy-items ? sell-items, such that
buy-price(item) sell-price(item).
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Matching
Price
Buy order
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Matching
Price
Buy order
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Fills
A fill is defined by a specific item and its price
, which must match the buy
order and the sell order
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Fills
Buy order Sports car 30,000
Sell order Mustang 28,000 or Corvette 32,000
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Attributes
A specific market is defined by a list of
attributes.
Example A used-car market is a set of all
possible vehicles, defined by model, year, and
mileage.
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Attributes
A trader specifies acceptableitems by attribute
values.
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Attributes
Sell order Model Mustang Year 2003
Price
Year
Buy order Model Mustang Year 2000..2003
03
02
01
00
Model
Camry
Mustang
Corvette
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Outline

• Motivation
• Main concepts
• Architecture
• Best-price matches
• Quality functions
• Performance
• Conclusions

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Architecture
The system consists of a central matcher anduser
interfaces that run on separate machines.
Matcher
User interface
User interface
User interface
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Data structures
The matcher includes a centralstructure for
indexing of orders.

• Tree of fully specified orders, which are
  called index orders

• Unordered list of the other orders, which are
  called nonindex orders

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Indexing tree
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Indexing tree
Model
Corvette
Mustang
Year
Year
1996
1997
1986
Mileage
Mileage
Mileage
50K
1996 Mustang, 50K miles, 5,000
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Trading cycle
The matcher alternates between processingnew
orders and identifying matches for old nonindex
orders.
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Processing
Process
For every new order Search for matches in
the indexing tree. If it is not filled, and
it is an index order, then add it to the
indexing tree. If it is not filled, and it is
a nonindex order, then add it to the
unordered list.
Re-match
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Re-matching
Process
For every old nonindex order Search for
matches in the indexing tree, among new
index orders. If it is filled, then
remove it from the unordered list.
Re-match
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Drawbacks
Process
Re-match

• The system does not find matches between two
  nonindex orders
• The system delays matches between a new index
  order and an old nonindex order

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Outline

• Motivation
• Main concepts
• Architecture
• Best-price matches
• Quality functions
• Performance
• Conclusions

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Optimal matches
The system searches for the best-price matches in
the indexing tree.

• Depth-first search

• Best-first search

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Depth-first search
Buy OrderAny car madeafter 1990
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Depth-first search
Drawback If there are many matching leaves, the
search takes a long time.
Solution Limit the number of matches.
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Depth-first search With limited number of matches
Buy OrderAny car madeafter 1990
Limit 2 matches
Actual best price
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Depth-first search With limited number of matches
Drawback The system may not find the best-price
match.
Solution Apply best-first search

• Store the best price for each subtree

• Use these prices to guide the search

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Best prices for subtrees
4,000
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Search for the best price
Buy OrderAny car madeafter 1990
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Search for the best price

• Advantages
• The system finds the best match
• It is much faster than DFS without a limit on
  the number of matches

• Drawback
• It is usually slower than DFS with a small
  limit on the number of matches

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Outline

• Motivation
• Main concepts
• Architecture
• Best-price matches
• Quality functions
• Performance
• Conclusions

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Quality functions
A trader can specify a quality function that
ranks the acceptable transactions.
The transaction quality may depend on an item and
its price.
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Quality functions
A trader can specify a quality function that
ranks the acceptable transactions.
The transaction quality may depend on an item and
its price.
Example Quality of a car purchase
4 for each year after 1970
5 for each 10K miles
6 for each 1,000
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Quality functions
A trader can specify a quality function that
ranks the acceptable transactions.
The transaction quality may depend on an item and
its price. The system searches for the matches
with the highest quality.
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Depth-first search
Buy OrderAny car madeafter 1990
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Monotonic attributes

• The quality monotonically changes with the
  price

• Usually, it is also monotonic on several
  other attributes

• Example
• Car quality
• Increases with the year
• Decreases with the mileage

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Best-first search

• For every subtree, store the best value of
  each monotonic attribute

• Use these values to estimate the quality of
  the best match in every subtree

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Best values for subtrees
2000, 10K, 4,000
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Search for the best match
Buy OrderAny car madeafter 1990
50K, 7,000
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Outline

• Motivation
• Main concepts
• Architecture
• Best-price matches
• Quality functions
• Performance
• Conclusions

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Performance
Experiments using aPentium computer

• 1.5 GHz CPU
• 1 Gbyte memory
• 166 MHz bus

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Variables

• Control variables
• Search strategy
• Number of orders
• Number of attributes

• Measurements
• Processing time
• Re-matching time
• Throughput

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Processing time
Process
Re-match
Logarithmic scale
Linear scale
1,000
400
10
300
time (sec)
200
0.1
100
0.001
0
1 10 100 1,000 10,000 100,000
50K 100K 150K 200K 250K
number of orders
number of orders
Best-First Search, Unlimited DFS, and Limited DFS
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Re-matching time
Process
Re-match
Logarithmic scale
Linear scale
1,000
400
10
300
time (sec)
200
0.1
100
0.001
0
1 10 100 1,000 10,000 100,000
50K 100K 150K 200K 250K
number of orders
number of orders
Best-First Search, Unlimited DFS, and Limited DFS
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Total time
Process
Re-match
Logarithmic scale
Linear scale
1,000
400
10
300
time (sec)
200
0.1
100
0.001
0
1 10 100 1,000 10,000 100,000
50K 100K 150K 200K 250K
number of orders
number of orders
Best-First Search, Unlimited DFS, and Limited DFS
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Throughput
100,000
10,000
1,000
orders per second
100
10
3
10
30
100
1
number of attributes
Best-First Search, Unlimited DFS, and Limited DFS
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Outline

• Motivation
• Main concepts
• Architecture
• Best-price matches
• Quality functions
• Performance
• Conclusions

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Summary

• General model for trading multi-attribute
  goods

• Hard and soft constrains in the specification
  of orders

• Fast identification of matches between buy
  and sell orders

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Other results

• Limited support for multi-order matches

Sell order 2 Mustangs 30,000
Buy order 1 Mustang 28,000
Buy order 1 Mustang 32,000
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Other results

• Limited support for multi-order matches
• Limited support for combinatorial orders

and
or
Sell order Camry 18,000
Buy order Mustang 28,000
Buy order Corvette 32,000
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Other results

• Limited support for multi-order matches
• Limited support for combinatorial orders
• Distributed broker modules

Matcher
Broker module
Broker module
User interface
User interface
User interface
User interface
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Current work

• Advanced indexing structures

• Search for approximate matches

• Trading different types of goods in a common
  exchange

• Integration with combinatorial auction
  algorithms

• Use of multiple matchers