Multi-Attribute Exchange Market: Search for Optimal Matches Eugene Fink Jianli Gong John Hershberger

Motivation Build an automated exchange for trading goods and services Combine the speed of the stock exchange with the flexibility of eBay +

Previous work Combinatorial auctions Standardized exchanges - Complex goods - Asymmetry between buyers and sellers - Illiquid - Simple goods - Symmetry between buyers and sellers - Liquid

Research goals Build an automated exchange for non-standardized goods. Support fast-paced trading for markets with millions of orders Include optimization techniques to maximize traders’ satisfaction

Outline Multi-attribute orders Best-price matches Quality functions Experimental results

Market A market is a set of items that can be traded, defined by a list of attributes. Example A used-car market is a set of all conceivable vehicles, defined by model, year, and mileage.

Orders A trader specifies a buy or sell order by attribute values and a price limit. Buy order Model: Mustang or Corvette Year: Mileage: 0..10K Price:  $32,000 Example Sell order Model: Mustang Year: 2004 Mileage: 1K Price:  $30,000 A value specification may include lists of values and numeric ranges.

Matching Year Model Price CamaroMustang Corvette $32,000 $30,000 Sell order Mustang, made in 2004, $30,000 Buy order Mustang, made after 2001, $32,000 Trade Mustang, made in 2004, $31,000

Outline Multi-attribute orders Best-price matches Quality functions Experimental results

Main structures Tree of fully specified orders Unordered list of the other orders

Depth-first search Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles, $7,000 Year Camry 1999 Mileage 1999 Camry, 10K miles, $18,000 10K Mileage Corvette, 20K miles, $4,000 20K Mileage Camry, 180K miles, $5, K Buy Order: Any car made after 1990 Best price

Depth-first search Drawback: If there are many matching leaves, the search takes a long time. Solution: Apply best-first search : Store the best price for each subtree Use these prices to guide the search

Best prices for subtrees Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles, $7,000 Year Camry 1999 Mileage 1999 Camry, 10K miles, $18,000 10K Mileage Corvette, 20K miles, $4,000 20K Mileage Camry, 180K miles, $5, K $7,000 $18,000 $5,000 $4,000 $7,000 $5,000 $4,000

Search for the best price Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles, $7,000 Year Camry 1999 Mileage 1999 Camry, 10K miles, $18,000 10K Mileage Corvette, 20K miles, $4,000 20K Mileage Camry, 180K miles, $5, K $7,000 $18,000 $5,000 $4,000 $7,000 $5,000 $4,000 Buy Order: Any car made after Camry, 180K miles, $5,000 Best price

Outline Multi-attribute orders Best-price matches Quality functions Experimental results

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

The transaction quality may depend on an item and its price. The system searches for the matches with the highest quality. Quality functions A trader can specify a quality function that ranks the acceptable transactions.

Depth-first search Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles, $7,000 Year Camry 1999 Mileage 1999 Camry, 10K miles, $18,000 10K Mileage Corvette, 20K miles, $4,000 20K Mileage Camry, 180K miles, $5, K Buy Order: Any car made after 1990 Quality: 37 Quality: 3Quality: 0 Highest quality: 37

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

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

Best values for subtrees Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles, $7,000 Year Camry 1999 Mileage 1999 Camry, 10K miles, $18,000 10K Mileage Corvette, 20K miles, $4,000 20K Mileage Camry, 180K miles, $5, K 2000, 10K, $4, , 20K, $4, , 10K, $5, , 50K, $7,000 20K, $4, K, $5,000 10K, $18,000 50K, $7,000

Search for the best match Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles, $7,000 Year Camry 1999 Mileage 1999 Camry, 10K miles, $18,000 10K Mileage Corvette, 20K miles, $4,000 20K Mileage Camry, 180K miles, $5, K 2000, 10K, $4, , 20K, $4, , 10K, $5, , 50K, $7,000 20K, $4, K, $5,000 10K, $18,000 50K, $7,000 Buy Order: Any car made after Highest quality: 37

Outline Multi-attribute orders Search for matches Quality functions Experimental results

Performance : 2 GHz CPU 1 Gbyte memory 166 MHz bus Experiments using a Pentium computer

Car market with eight attributes number of orders orders per second : 200 to 20,000 orders per second Cars and bonds : 500 to 50,000 orders per second bonds Bond market with two attributes cars

Artificial markets Synthetic market data: 1 to 100 attributes 300,000 orders Best-First Depth-First number of attributes orders per second

Summary General model for trading of multi-attribute goods Fast identification of matches between buy and sell orders