Market Madness: Implementing a 9.2 quintillion outcome prediction market David Pennock

Market Madness: Implementing a 9.2 quintillion outcome prediction market

David Pennock

ResearchResearch

A (2-outcome) prediction market

• A random variable, e.g.

• Turned into a financial instrument payoff = realized value of variable

$1 if $0 if

I am entitled to:

2010 the warmest year on record?(Y/N)

2010 thewarmest

not thewarmest

ResearchResearch

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http://intrade.com

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AAAI’04 July 2004 MP1-4

Another example: Options Options prices (partially) encode a probability

distribution over their underlying stocks

stock price s10 20 30 40 50

call20=max[0,s-20]

payoff

call30=max[0,s-30]

call40=max[0,s-40]

AAAI’04 July 2004 MP1-5

Another example: Options Options prices (partially) encode a probability

distribution over their underlying stocks

stock price s10 20 30 40 50

call20

payoff

- 2*call30 + call40

“butterfly spread”

AAAI’04 July 2004 MP1-6

Another example: Options Options prices (partially) encode a probability

distribution over their underlying stocks

stock price s10 20 30 40 50

call30

payoff

- 2*call40 + call50

AAAI’04 July 2004 MP1-7

Another example: Optionscall10 - 2 call20 + call30 = $2.13 relative

call30 - 2 call30 + call40 = $5.73 likelihood of falling

call30 - 2 call40 + call50 = $3.54 near center

stock price s10 20 30 40 50

payoff

$2.13 $5.73 $3.54

Reinventing the wheel

• Put prices:CDF (PDF) of stock price

• Butterfly spreads:discrete approx of PDF

• PDF of stocks are ~lognormal

Reinventing the wheel

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lognormal(u=3.67, =.205)

Bid,ask,mid of butterfly spreads

Put pricesBest fit lognormal

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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

The outrage II

Range bets require four trades

– Four commisions, four bid-ask spreads

– Execution risk

stock price s10 20 30 40 50

call20

payoff

- 2*call30 + call40

“butterfly spread”

AAAI’04 July 2004 MP1-12

Example: Options

YHOOstock price s

10 20 30 40 50

payoff

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AAAI’04 July 2004 MP1-13

Example: Options

YHOOstock price s

10 20 30 40 50

payoff

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AAAI’04 July 2004 MP1-14

Example: OptionsQuickTime™ and aTIFF (LZW) decompressor

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The thesis

• In a well designed (derivative) market

information is everythinginformation is the only thing

• Contrapositive:redundancy = poor design

Continuous double auctionUber-hammer of the financial world

• Used everywhere– Stocks, options, futures, derivatives

– Gambling: BetFair, InTrade

• Related bets? Just use two CDAs– Max[YHOO-10], Max[YHOO-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’

Continuous double auctionUber-hammer of the financial world

• CDA was invented when auctioneers were people

• Had to be dead simple

• Today, auctioneers are computers...

• ...Yet CDA remains the standard

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Example:

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Example: Bet365

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ResearchResearchExample: Y! Predictalot

ResearchResearch

9.2 quintillion outcomes

Example: Y! Predictalot

ResearchResearch

The pitch (to gamers)

• Predict any property2263 possible in theory [gogol,gogolplex]• Duke wins >3 games• Duke wins more than UNC, less than NCST• Sum (seeds of ACC teams in final8) is prime

• We’ll instantly quote odds for any of them• Effects related predictions automatically

• Predict Duke wins tournamentOdds Duke wins rnd 1 goes up

ResearchResearch

The pitch (to economists)

• Information is everything• Traders (people) focus on information

Provide it in whatever form they like• Mechanism (computer) handles logical &

Bayesian propagation - what it’s good at

• No redundancy, no exec risk, everything is 1 trade

Overview: Complexity Results

Permutations Boolean Taxonomy

General Pair Subset General 2-clause Restrict

Tourney

General Tree

Auction-eer

NP-hard

EC’07

NP-hard

EC’07

Poly

EC’07

NP-hard

DSS’05

co-NP-complete

DSS’05

? ? ?

Market Maker

(LMSR)

#P-hard

EC’08

#P-hard

EC’08

#P-hard

EC’08

#P-hard

EC’08

Approx

STOC’08

#P-hard

EC’08

Poly

STOC’08

#P-hard

AAMAS‘09

Poly

AAMAS‘09

LMSR market maker

• Robin Hanson: Logarithmic market scoring rule market maker

Event = E = e.g. Duke wins > 3Outcome = o = complete unfolding of tourn

oEeqo/b

oTRUEeqo/bPrice of E =

LMSR market maker

• oEeqo/b

oTRUEeqo/b

• Impossible: Store 263 numbers

• Complex: Sum over 263 numbers

• Doable: Approx sum over 263 nums*tricks required to do it well/fast

Main loop

Input: event E

for 1 to NUM_SAMPLESsample oforeach bet (F,qF)

qo+=qF if oFnumer += eqo/b/p(o) if oEdenom += eqo/b/p(o)

return numer/denom

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

Sampling

• Sampling is accurate when outcomes are chosen proportional to eq/b

• Can’t 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

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

Eval

• If E is a snippet of code, then testingoE 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

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 code;Google open social

– Small view on my.yahoo, yahoo.com (330M)

– Activity stream can appear across Y!(e.g., mail, sports, finance, profiles)

The modal dialog opens with a screen to select a

prediction type

The modal dialog opens with a screen to select a

prediction type

Example: Y! Predictalot

On selecting the template for prediction type the other

controls are displayed progressively

On selecting the template for prediction type the other

controls are displayed progressively

Example: Y! Predictalot

Here the user then sets the prediction parameters, but

note that the ‘make prediction’ button is disabled

till all parameters are set

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

Odds are calculated only after the user finalizes on

the prediction

Odds are calculated only after the user finalizes on

the prediction

Example: Y! Predictalot

Example: Y! Predictalot

Finally once investments are placed the ‘Make prediction’

button gets enabled.

Finally once investments are placed the ‘Make prediction’

button gets enabled.

Example: Y! Predictalot

Example: Y! Predictalot

What’s 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

More

What is (and what good is) a combinatorial prediction market?

http://blog.oddhead.com/2008/12/22/what-is-and-what-good-is-a-combinatorial-prediction-market/

ResearchResearch

A research agenda:

Chance 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, adversarial ML

• Out: Roulette, human poker, chess

A research methodology

Design Build Analyze

HSXNFTS

WSEXFXPS

Examples

Design

• Prediction markets– Dynamic parimutuel

– Combinatorial bids

– Combinatorial outcomes

– Shared scoring rules

– Linear programming backbone

• Ad auctions

• Spam incentives

Build Analyze

• Computational complexity

• Does money matter?

• Equilibrium analysis

• Wisdom of crowds: Combining experts

• Practical lessons

• Predictalot

• Yoopick

• Y!/O Buzz

• Centmail

• Pictcha

• Yootles

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The evolution of markets

• Phase 0: Invention, manual execution

Auctions

Finance

WALL STREET

Advertising

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bookstores, banks, grocery stores, ...

The evolution of markets

• Phase 1: Computers mimic it(Cheaper, faster)

Auctions

Finance

ECN

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Amazon, ATMs, auto checkout, ...

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The evolution of markets

• Phase 2: Computers improve it(Cheaper, faster, better)

AuctionsFinance

Advertising

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Source: Sandholm, T. “Expressive Commerce andIts Application to Sourcing: How We Conducted$35 Billion of Generalized Combinatorial Auctions.”AI Magazine, 28(3): 45-58, 2007

Expressive auctions for chemicals,packaging, ingredients, technology,services, medical, transport, materials, ...

custom Amazon, e-banking, RFID, ...

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ResearchResearch

Phase 0

Mechanism(Rules)

e.g. Auction,Exchange, ...

ResearchResearch

Phase 1

Mechanism(Rules)

e.g. Auction,Exchange, ...

ResearchResearch

Phase 1.5

Mechanism(Rules)

e.g. Auction,Exchange, ...

Stats/ML/OptEngine

Stats/ML/OptEngine

Stats/ML/OptEngine

Stats/ML/OptEngine

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Phase 2

Mechanism(Rules)

e.g. Auction,Exchange, ...

Stats/ML/OptEngine

Stats/ML/OptEngine

Stats/ML/OptEngine

Stats/ML/OptEngine

Stats/ML/OptEngine

ResearchResearch

Phase 2

Mechanism(Rules)

e.g. Auction,Exchange, ...

Stats/ML/OptEngine

Stats/ML/OptEngine

Stats/ML/OptEngine

Stats/ML/OptEngine

Stats/ML/OptEngine

Advertising, Finance, ...