Research
Computational Aspects of
Prediction Markets
David M. Pennock, Yahoo! Research
Yiling Chen, Lance Fortnow, Joe Kilian,
Evdokia Nikolova, Rahul Sami, Michael Wellman
Research
Mech Design for Prediction
• Q: Will there be a bird flu outbreak in
the US in 2007?
• A: Uncertain. Evidence distributed:
health experts, nurses, public
• Goal: Obtain a forecast as good as
omniscient center with access to all
evidence from all sources
Research
A Prediction Market
• Take a random variable, e.g.
Bird Flu Outbreak US 2007?
(Y/N)
• Turn it into a financial instrument
payoff = realized value of variable
I am entitled to:
$1 if
Bird Flu
US ’07
$0 if
Bird Flu
US ’07
Research
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http://intrade.com
Screen capture 2007/04/19
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Research
Mech Design for Prediction
• Standard Properties • PM Properties
•
•
•
•
•
Efficiency
Inidiv. rationality
Budget balance
Revenue
Comp. complexity
• Equilibrium
• General, Nash, ...
•
•
•
•
•
•
#1: Info aggregation
Expressiveness
Liquidity
Bounded budget
Indiv. rationality
Comp. complexity
• Equilibrium
• Rational
expectations
Competes with:
experts, scoring
rules, opinion
pools, ML/stats,
polls, Delphi
Research
Mech Design for Prediction
Financial Markets
Prediction Markets
Primary
Social welfare (trade)
Hedging risk
Information aggregation
Secondary
Information aggregation
Social welfare (trade)
Hedging risk
Research
Outline
• Examples, research overview
• Some computational aspects of PMs
• Combinatorics
• Betting on permutations
• Betting on Boolean expressions
• Automated market makers
• Hanson’s market scoring rule
• Dynamic parimutuel market
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http://intrade.com
http://tradesports.com
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http://www.biz.uiowa.edu/iem
http://www.wsex.com/
IPO
Play money;
Real predictions
http://www.hsx.com/
http://www.ideosphere.com
Cancer
cured
by 2010
Machine Go
champion
by 2020
http://us.newsfutures.com/
Research
Yahoo!/O’Reilly Tech Buzz Game
http://buzz.research.yahoo.com/
[Source: Berg, DARPA Workshop, 2002]
Research
Example: IEM 1992
[Source: Berg, DARPA Workshop, 2002]
Research
Example: IEM
[Source: Berg, DARPA Workshop, 2002]
Research
Example: IEM
Research
Prediction Accuracy
Market Forecast Winning Probability and Actual Winning Probability
100
Prices: TradeSports and NewsFutures
100
Fitted Value: Linear regression
45 degree line
TradeSports: Correlation=0.96
NewsFutures: Correlation=0.94
90
75
TradeSports Prices
80
70
60
50
40
50
25
30
20
10
0
0
0
10
20
30
40
50
60
70
Trading Price Prior to Game
80
90
0
100
20
40
60
NewsFutures Prices
n=416 over 208 NFL games.
Correlation between TradeSports and NewsFutures prices = 0.97
Data are grouped so that prices are rounded to the nearest ten percentage points; n=416 teams in 208 games
Rank
Prediction Performance of Markets
Relative to Individual Experts
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
NewsFutures
Tradesports
1
2
3
4
5
6
7
8
9 10 11 12 13 14
Week into the NFL season
80
100
Does it work?
Yes...
• Evidence from real markets, laboratory experiments, and theory
indicate that markets are good at gathering information from
many sources and combining it appropriately; e.g.:
– Markets like the Iowa Electronic Market predict election outcomes
better than polls
[Forsythe 1992, 1999][Oliven 1995][Rietz 1998][Berg 2001][Pennock 2002]
– Futures and options markets rapidly incorporate information,
providing accurate forecasts of their underlying
commodities/securities
[Sherrick 1996][Jackwerth 1996][Figlewski 1979][Roll 1984][Hayek 1945]
– Sports betting markets provide accurate forecasts of game outcomes
[Gandar 1998][Thaler 1988][Debnath EC’03][Schmidt 2002]
Does it work?
Yes...
• E.g. (cont’d):
– Laboratory experiments confirm information aggregation
[Plott 1982;1988;1997][Forsythe 1990][Chen, EC-2001]
– And field tests [Plott 2002]
– Theoretical underpinnings: “rational expectations”
[Grossman 1981][Lucas 1972]
– Procedural explanation: agents learn from prices
[Hanson 1998][Mckelvey 1986][Mckelvey 1990][Nielsen 1990]
– Proposals to use information markets to help science [Hanson 1995],
policymakers, decision makers [Hanson 1999], government [Hanson 2002],
military [DARPA FutureMAP, PAM]
– Even market games work! [Servan-Schreiber 2004][Pennock 2001]
Research
Predicting Permutations
• Predict the ordering of a set of
statistics
•
•
•
•
Horse race finishing times
Daily stock price changes
NFL Football quarterback passing yards
Any ordinal prediction
• Chen, Fortnow, Nikolova, Pennock,
EC’07
Research
Market Combinatorics
Permutations
• A>B>C
• A>C>B
• B>A>C
.1
.2
.1
• B>C>A
• C>A>B
• C>B>A
.3
.1
.2
Research
Market Combinatorics
Permutations
•
•
•
•
•
•
•
•
•
•
•
•
D>A>B>C
D>A>C>B
D>B>A>C
A>D>B>C
A>D>C>B
B>D>A>C
A>B>D>C
A>C>D>B
B>A>D>C
A>B>C>D
A>C>B>D
B>A>C>D
.01
.02
.01
.01
.02
.05
.01
.2
.01
.01
.02
.01
•
•
•
•
•
•
•
•
•
•
•
•
D>B>C>A
D>C>A>B
D>C>B>A
B>D>C>A
C>D>A>B
C>D>B>A
B>C>D>A
C>A>D>B
C>B>D>A
B>C>D>A
C>A>D>B
C>B>D>A
.05
.1
.2
.03
.1
.02
.03
.01
.02
.03
.01
.02
Research
Bidding Languages
• Traders want to bet on properties of
orderings, not explicitly on orderings: more
natural, more feasible
• A will win ; A will “show”
• A will finish in [4-7] ; {A,C,E} will finish in top 10
• A will beat B ; {A,D} will both beat {B,C}
• Buy 6 units of “$1 if A>B” at price $0.4
• Supported to a limited extent at racetrack
today, but each in different betting pools
• Want centralized auctioneer to improve
liquidity & information aggregation
Research
Auctioneer Problem
• Auctioneer’s goal:
Accept orders with non-negative
worst-case loss (auctioneer never
loses money)
• The Matching Problem
• Formulated as LP
• Generalization: Market Maker Problem:
Accept orders with bounded worst-case loss
(auctioneer never loses more than b dollars)
Research
Example
• A three-way match
• Buy 1 of “$1 if A>B” for 0.7
• Buy 1 of “$1 if B>C” for 0.7
• Buy 1 of “$1 if C>A” for 0.7
B
A
C
Research
Pair Betting
• All bets are of the form “A will beat B”
• Cycle with sum of prices > k-1 ==> Match
(Find best cycle: Polytime)
• Match =/=> Cycle with sum of prices > k-1
• Theorem: The Matching Problem for Pair
Betting is NP-hard (reduce from min
feedback arc set)
Research
Subset Betting
• All bets are of the form
• “A will finish in positions 3-7”, or
• “A will finish in positions 1,3, or 10”, or
• “A, D, or F will finish in position 2”
• Theorem: The Matching Problem for Subset
Betting is polytime (LP + maximum
matching separation oracle)
Research
Market Combinatorics
Boolean
I am entitled to:
$1 if A1&A2&…&An
I am entitled to:
$1 if A1&A2&…&An
I am entitled to:
$1 if A1&A2&…&An
I am entitled to:
$1 if A1&A2&…&An
I am entitled to:
$1 if A1&A2&…&An
I am entitled to:
$1 if A1&A2&…&An
I am entitled to:
$1 if A1&A2&…&An
I am entitled to:
$1 if A1&A2&…&An
• Betting on complete conjunctions is both
unnatural and infeasible
Research
Market Combinatorics
Boolean
• A bidding language: write your own security
I am entitled to:
$1 if Boolean_fn | Boolean_fn
• For example
I am entitled to:
$1 if A1 | A2
I am entitled to:
$1 if (A1&A7)||A13 | (A2||A5)&A9
I am entitled to:
$1 if A1&A7
• Offer to buy/sell q units of it at price p
• Let everyone else do the same
• Auctioneer must decide who trades with
whom at what price… How? (next)
• More concise/expressive; more natural
Research
The Matching Problem
• There are many possible matching rules for
the auctioneer
• A natural one: maximize trade subject to
no-risk constraint
trader gets $$ in state:
• Example:
• buy 1 of
• sell 1 of
• sell 1 of
for $0.40
$1 if A1
for $0.10
$1 if A1&A2
for $0.20
$1 if A1&A2
• No matter what happens,
auctioneer cannot lose
money
A1A2 A1A2 A1A2 A1A2
0.60 0.60 -0.40 -0.40
-0.90 0.10 0.10 0.10
0.20 -0.80 0.20 0.20
-0.10 -0.10 -0.10 -0.10
Research
Market Combinatorics
Boolean
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Research
Fortnow; Kilian; Pennock; Wellman
Complexity Results
• Divisible orders: will accept any q*  q
• Indivisible: will accept all or nothing
reduction from X3C
LP
# events
O(log n)
O(n)
divisible
polynomial
co-NP-complete
reduction from SAT
• Natural algorithms
indivisible
NP-complete
2p complete
reduction from TBF
• divisible: linear programming
• indivisible: integer programming;
logical reduction?
Research
[Thanks: Yiling Chen]
Automated Market Makers
•
A market maker (a.k.a. bookmaker) is a firm or person who is
almost always willing to accept both buy and sell orders at
some prices
Why an institutional market maker? Liquidity!
•
•
•
•
•
Without market makers, the more expressive the betting
mechanism is the less liquid the market is (few exact matches)
Illiquidity discourages trading: Chicken and egg
Subsidizes information gathering and aggregation: Circumvents
no-trade theorems
Market makers, unlike auctioneers, bear risk. Thus, we desire
mechanisms that can bound the loss of market makers
•
Market scoring rules [Hanson 2002, 2003, 2006]
•
Dynamic pari-mutuel market [Pennock 2004]
Research
Pari-Mutuel Market
Basic idea
1
1
Research
Dynamic Parimutuel Market
C(1,2)=2.2
C(2,3)=3.6
C(2,2)=2.8
C(2,4)=4.5
C(3,8)=8.5
C(4,8)=8.9
C(2,5)=5.4
C(5,8)=9.4
C(2,6)=6.3
C(2,7)=7.3
C(2,8)=8.2
Research
Share-ratio price function
• One can view DPM as a market maker
n
• Cost Function:
2
C (Q )   qi
i 1
• Price Function:
• Properties
•
•
•
•
pi (Q ) 
qi
n
qj
No arbitrage
pricei/pricej = qi/qj
pricei < $1
payoff if right = C(Qfinal)/qo > $1
j 1
2
Research
Open Questions
Combinatorial Betting
• Usual hunt: Are there natural, useful,
expressive bidding languages (for
permutations, Boolean, other) that
admit polynomial time matching?
• Are there good heuristic matching
algorithms (think WalkSAT for
matching); logical reduction?
• How can we divide the surplus?
• What is the complexity of incremental
matching?
Research
Open Questions
Automated Market Makers
• For every bidding language with
polytime matching, does there exist a
polytime MSR market maker?
• The automated MM algorithms are
online algorithms: Are there other
online MM algorithms that trade more
for same loss bound?
Research
http://buzz.research.yahoo.com
•
•
•
Yahoo!,O’Reilly launched Buzz Game 3/05 @ETech
Research testbed for investigating prediction markets
Buy “stock” in hundreds of technologies
•
Earn dividends based on actual search “buzz”
•
•
API interface
Exchange mechanism is dynamic parimutuel market
Cross btw stock market and horse race betting
Research
Yahoo!/O’Reilly Tech Buzz Game
http://buzz.research.yahoo.com/
Research
Technology forecasts
• iPod phone
• What’s next?
Google Calendar?
price
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search
buzz
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8/28: buzz gamers
begin bidding
up iPod phone
8/29: Apple
invites press
to “secret”
unveiling
9/7: Apple
announces
Rokr
9/8-9/18: searches
for iPod phone soar;
early buyers profit
• Another Apple unveiling
10/12; iPod Video?
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9am 10/5
Analysis
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Research
Tech Buzz Game