Exchanges for Complex Commodities: Toward a General-Purpose System Committee: Eugene Fink Rafael Perez Dmitry B. Goldgof John Hershberger

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

Outline Previous work

One-attribute market Outline

Previous work One-attribute market Multi-attribute market Outline

Previous work One-attribute market Multi-attribute market Large number of attributes Outline

Previous work One-attribute market Multi-attribute market Large number of attributes Numeric attributes Outline

Previous work One-attribute market Multi-attribute market Large number of attributes Numeric attributes Complex orders Outline

Previous work One-attribute market Multi-attribute market Large number of attributes Numeric attributes Complex orders Price functions Outline

Previous work One-attribute market Multi-attribute market Large number of attributes Numeric attributes Complex orders Price functions Main results Outline

Combinatorial auctions Complex commodities Asymmetry between buyers and sellers Illiquid

Standardized exchanges Simple commodities Symmetry between buyers and sellers Liquid

One-attribute market Price Buy order Stock symbol $89.02 Price Sell order Stock symbol GEIBM MCD GEIBM MCD $89.00

One-attribute market Price Stock symbol GEIBM MCD $89.02 Buy order Sell order $89.00

Table of items Table of all tradable items BA GE IBM PG MCD $88.94 $88.93$88.97 $88.92$88.93 $88.96$88.99 For each item, a tree of prices

Multi-attribute market Mileage Buy order Model Year Mustang 50, Mileage Sell order Model Year 30, Echo Corvette Camaro Camry Echo Mustang Camry Camaro Corvette

Multi-attribute market Mileage Model Year Mustang 50, Echo Camry 30,000 Corvette Camaro

Retrieval tree Retrieval tree (a.k.a. trie) of simple orders Year 1999 Year Camry Model CorvetteMustang Mileage 1999 Camry, 10K miles, $18,000 10K Mileage 50K 1996 Mustang, 50K miles, $7,000 Mileage 1988 Corvette, 20K miles, $4,000 20K Mileage 2000 Camry, 180K miles, $5, K

Main structures Trie of simple orders List of complex 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 With limited number of matches 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 among found matches Actual best price Limit: 2 matches

Large number of attributes Model Corvette Year Camry 1999 Mileage 10K Mileage K Cylinders 64 Mileage Year K Cylinders Mustang 50K miles, 4 cyl. Year Mileage K Cylinders Corvette 20K miles, 8 cyl. Mustang 1999 Camry 10K miles, 6 cyl Camry 180K miles, 4 cyl.

PATRICIA Model Year Camry 1999, 10K, , 180K, Mustang 50K miles, 4 cyl Corvette 20K miles, 8 cyl. Mustang, 1996, 50K, Camry 10K miles, 6 cyl Camry 180K miles, 4 cyl. Corvette, 1988, 20K, 8

Numeric attributes Mileage Top speed MPG , Mileage Sell order Top speed MPG 30,000 Buy order

Numeric attributes Mileage Top speed MPG , ,000

PATRICIA with numeric attributes PATRICIA gives high branching factor Mileage 100K, 20, K miles, 25 MPG, 140 m.p.h. 100K miles, 20 MPG, 110 m.p.h. 10K, 25, K miles, 28 MPG, 90 m.p.h. 90K, 18, K miles, 18 MPG, 100 m.p.h. 30K, 28, 90

KD -trees Miles MPG Car 1 50K45 Car 3 70K25 Car 4 90K 34 Car 5 30K16 Car 6 40K10 Car 2 20K18 MPG K20K40K60K80K (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Miles Tree for handling numeric attributes

MPG (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 20K40K60K80K Miles KD -trees 0100K

KD -trees MPG (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 2 20K40K60K80K Miles 0100K

KD -trees MPG (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 2 Car 3 20K40K60K80K Miles 0100K

KD -trees MPG (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 2 Car 3 Car 4 20K40K60K80K Miles 0100K

KD -trees MPG (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 5 Car 2 Car 3 Car 4 20K40K60K80K Miles 0100K

KD -trees Car 1 Car 5 Car 2 Car 3 Car 4 Car 6 MPG (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 20K40K60K80K Miles 0100K

KD -trees MPG (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 5 Car 2 Car 3 Car 4 Car 6 20K40K60K80K Miles 0100K

Complex orders Mileage MPG Mileage MPG 50,000 Sell order 50,000 25,000 Buy order Top speed Top speed

Complex orders MPG Mileage 50,000 25,000 Top speed

Indexing of complex orders Miles (K) MPG Car 1 40–6040–50 Car 3 52–8820–30 Car 4 80–99 24–44 Car 5 25–3511–21 Car 6 34–465–15 Car 2 12–2813–23

Indexing of complex orders MPG 50 20K40K60K80K Car 1 Car 2 Car 3 Car 4 Car 5 Car 6 Miles Car 1 Car 5 Car 2 Car 3 Car 4 Car K

Price functions Year Model Price CamaroMustangCorvette $32K $30K $28K $30K $32K Price limit: $32K – (2003 – Year) · $2K Order: Mustang

Price functions Year Model Price CamaroMustangCorvette $32K $30K $28K $30K $32K Sell order Mustang made in 2003 Price = $30,000 Buy order Mustang Price = $32K – (2003 – Year) · $2K

Price functions Orders with identical attributes are in the same leaf Each leaf includes a tree of prices

Leaf nodes Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage Corvette, 20K miles 20K Mileage Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

Leaf nodes Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage Corvette, 20K miles 20K Mileage Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

Leaf nodes Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage Corvette, 20K miles 20K Mileage Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

Leaf nodes Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage Corvette, 20K miles 20K Mileage Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

Leaf nodes Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage Corvette, 20K miles 20K Mileage Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

Leaf nodes Model Mileage Year CorvetteMustang K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage Corvette, 20K miles 20K Mileage Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990 Best Match

Main results Formalization of previous techniques Identification of open problems Theoretical solutions to some problems

Future work (Ph.D.) Advanced indexing structures Search for approximate matches Trading different commodity types in a common exchange