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## Market Madness: Implementing a 9.2 quintillion outcome prediction market

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### Market Madness: Implementing a 9.2 quintillion outcome prediction market David Pennock A (2-outcome) prediction market A random variable, e.g. Turned into a financial ... – PowerPoint PPT presentation

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Title: Market Madness: Implementing a 9.2 quintillion outcome prediction market

1
Market Madness Implementing a 9.2 quintillion
outcome prediction market
• David Pennock

2
A (2-outcome) prediction market
• A random variable, e.g.
• Turned into a financial instrument payoff
realized value of variable

2010 the warmest year on record?(Y/N)
I am entitled to
2010 thewarmest
not thewarmest
1 if
0 if
3
2010
4
Another example Options
• Options prices (partially) encode a probability
distribution over their underlying stocks

payoff
10
20
30
40
50
stock price s
5
Another example Options
• Options prices (partially) encode a probability
distribution over their underlying stocks

payoff
10
20
30
40
50
stock price s
- 2call30
6
Another example Options
• Options prices (partially) encode a probability
distribution over their underlying stocks

payoff
10
20
30
40
50
stock price s
- 2call40
7
Another example Options
• call10 - 2 call20 call30 2.13
relative
• call30 - 2 call30 call40 5.73 likelihood
of falling
• call30 - 2 call40 call50 3.54 near
center

payoff
2.13
5.73
3.54
10
20
30
40
50
stock price s
8
Reinventing the wheel
• Put prices?CDF (??PDF) of stock price
• Butterfly spreadsdiscrete approx of PDF
• PDF of stocks are lognormal

9
Reinventing the wheel
• Put pricesBest fit ??lognormal
• lognormal(u3.67, ?.205)

10
The outrage
• What about call prices?ENTIRELY REDUNDANT!
• I know that, you say put-call parity
• From an information standpoint, they are useless
• From a trading standpoint, they might be useful,
but only because markets are poorly designed

11
The outrage II
• Range bets require four trades
• Execution risk

12
Example Options
payoff
10
20
30
40
50
YHOOstock price s
13
Example Options
payoff
10
20
30
40
50
YHOOstock price s
14
Example Options
15
The thesis
• In a well designed (derivative)
marketinformation is everythinginformation is
the only thing
• Contrapositiveredundancy poor design

16
Continuous double auctionUber-hammer of the
financial world
• Used everywhere
• Stocks, options, futures, derivatives
• Gambling BetFair, InTrade
• Related bets? Just use two CDAs
• MaxYHOO-10, MaxYHOO-20
• Horse wins, Horse finishes 1st or 2nd
• Power set instruments Mutual funds, ETFs,
butterfly spreads, Western Conference wins
• Treats everything like apples and oranges, even
fish and fish and chips

17
Continuous double auctionUber-hammer of the
financial world
• CDA was invented when auctioneers were people
• Today, auctioneers are computers...
• ...Yet CDA remains the standard

18
Example
19
Example Bet365
20
Example Y! Predictalot
21
Example Y! Predictalot
• 9.2 quintillion outcomes

22
The pitch (to gamers)
• Predict any property2263 possible in theory
gogol,gogolplex
• Duke wins gt3 games
• Duke wins more than UNC, less than NCST
• Sum (seeds of ACC teams in final8) is prime
• Well instantly quote odds for any of them
• Effects related predictions automatically
• Predict Duke wins tournament?Odds Duke wins rnd
1 goes up

23
The pitch (to economists)
• Information is everything
• Traders (people) focus on informationProvide it
in whatever form they like
• Mechanism (computer) handles logical Bayesian
propagation - what its good at
• No redundancy, no exec risk, everything is 1

24
Overview Complexity Results
Permutations Permutations Permutations Boolean Boolean Boolean Taxonomy Taxonomy Taxonomy
General Pair Subset General 2-clause Restrict Tourney General Tree
Auction-eer NP-hard EC07 NP-hard EC07 Poly EC07 NP-hard DSS05 co-NP-complete DSS05 ? ? ?
Market Maker (LMSR) P-hard EC08 P-hard EC08 P-hard EC08 P-hard EC08 Approx STOC08 P-hard EC08 Poly STOC08 P-hard AAMAS09 Poly AAMAS09
25
LMSR market maker
• Robin Hanson Logarithmic market scoring rule
market makerEvent E e.g. Duke wins gt
3Outcome o complete unfolding of tourn
?o?Eeqo/b ?o?TRUEeqo/b

Price of E
26
LMSR market maker
• ?o?Eeqo/b ?o?TRUEeqo/b
• Impossible Store 263 numbers
• Complex Sum over 263 numbers
• Doable Approx sum over 263 numstricks required
to do it well/fast

27
Main loop
• Input event E
• for 1 to NUM_SAMPLESsample oforeach bet
(F,qF) qoqF if o?Fnumer eqo/b/p(o) if
o?Edenom eqo/b/p(o)
• return numer/denom

28
Other market maker functions
• Point price is all we need!
• From price we can compute
• Total cost of any number of shares qE
• Number of shares purchasable for any dollar
amount (inverse cost)
• New price after purchasing qE shares

29
Sampling
• Sampling is accurate when outcomes are chosen
proportional to eq/b
• Cant be done (P-hard)
• Can sample proportion to q, if size of event is
known
• For now, we sample according to seed-based prior
fit to historical data
• Next Metropolis-Hastings

30
Sampling
• No guarantees
• Erratic convergencee10 dwarfs e8
• Linear scan of all bets in inner loop!
• Now getting serious about improving sampling 1)
fast, 2) stable, 3) accurate

31
Eval
• If E is a snippet of code, then testingo?E
requires an eval of the code
• Slow in interpreted languages can be gamed
serious security risk
• Proceeded in phases 1) Mathematica, 2) PHP, 3)
Now implemented a mini language parser in Java
much faster

32
Demo
• With Mani Abrol, Janet George, Tom Gulik, Mridul
Muralidharan, Sudar Muthu, Navneet Nair, Abe
Othman, David Pennock, Daniel Reeves, and Pras
Sarkar
• Yahoo! Application Platform
• Takes care of login/auth, friends, sharing
• Easy to create good sample codeGoogle open
social
• Small view on my.yahoo, yahoo.com (330M)
• Activity stream can appear across Y!(e.g., mail,
sports, finance, profiles)

33
The modal dialog opens with a screen to select a
prediction type
Example Y! Predictalot
34
On selecting the template for prediction type the
other controls are displayed progressively
Example Y! Predictalot
35
Here the user then sets the prediction
parameters, but note that the make prediction
button is disabled till all parameters are set
Example Y! Predictalot
36
Odds are calculated only after the user finalizes
on the prediction
Example Y! Predictalot
37
Example Y! Predictalot
38
Finally once investments are placed the Make
prediction button gets enabled.
Example Y! Predictalot
39
Example Y! Predictalot
40
Whats next
• Road to March Built it, now we hope you come! (
promo from Y!Sports)
• Road to June World CupThen IPL, NFL?, Oscars?,
Politics?
• Sampling tricks art and science
• MM to revenue positive proof of concept
• Flexible market maker Abe Othman
• Other price functions dynamic parimutuel
• Open puzzles integrating limit and market
orders, interval bets on real line

41
More
• What is (and what good is) a combinatorial
prediction market?
at-good-is-a-combinatorial-prediction-market/

42
A research agendaChance Tech
• Technology to
• Manage chance prediction, finance
• Mitigate chance insurance
• Manufacture chance gambling
• In Wisdom of crowds, prediction markets, stock
picking, money management, online betting
exchanges, computer poker, custom insurance,
• Out Roulette, human poker, chess

43
A research methodology
HSX
Design
Build
Analyze
NF
TS
WSEX
FX
PS
44
Examples
Design
Build
Analyze
• Prediction markets
• Dynamic parimutuel
• Combinatorial bids
• Combinatorial outcomes
• Shared scoring rules
• Linear programming backbone
• Spam incentives
• Computational complexity
• Does money matter?
• Equilibrium analysis
• Wisdom of crowds Combining experts
• Practical lessons
• Predictalot
• Yoopick
• Y!/O Buzz
• Centmail
• Pictcha
• Yootles

45
The evolution of markets
• Phase 0 Invention, manual execution

Auctions
FinanceWALL STREET
bookstores, banks, grocery stores, ...
46
The evolution of markets
• Phase 1 Computers mimic it (Cheaper, faster)

Auctions
FinanceECN
Amazon, ATMs, auto checkout, ...
47
The evolution of markets
• Phase 2 Computers improve it (Cheaper,
faster, better)

Auctions
Expressive auctions for chemicals,packaging,
ingredients, technology,services, medical,
transport, materials, ...
Finance
Source Sandholm, T. Expressive Commerce andIts
Application to Sourcing How We Conducted35
Billion of Generalized Combinatorial
Auctions.AI Magazine, 28(3) 45-58, 2007
custom Amazon, e-banking, RFID, ...
48
Phase 0
Mechanism(Rules) e.g. Auction,Exchange, ...
49
Phase 1
Mechanism(Rules) e.g. Auction,Exchange, ...
50
Phase 1.5
Mechanism(Rules) e.g. Auction,Exchange, ...
51
Phase 2
Mechanism(Rules) e.g. Auction,Exchange, ...
52
Phase 2