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A tractable combinatorial market maker using constraint generation

A tractable combinatorial market maker using constraint generation. MIROSLAV DUDÍK, SEBASTIEN LAHAIE, DAVID M. PENNOCK Microsoft Research. Thanks: David Rothschild, Dan Osherson , Arvid Wang, Jake Abernethy, Rafael Frongillo , Rob Schapire.

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A tractable combinatorial market maker using constraint generation

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  1. A tractable combinatorial market maker using constraint generation MIROSLAV DUDÍK, SEBASTIEN LAHAIE,DAVID M. PENNOCK Microsoft Research Thanks: David Rothschild, Dan Osherson, Arvid Wang, Jake Abernethy, Rafael Frongillo, Rob Schapire

  2. A combinatorial question:How pivotal was Ohio? • Day before the election: • 83.1% chance that whoever wins Ohio will win the election • If Obama wins Ohio, 93.9% chance he’ll win the election • If Romney wins Ohio, 53.2% chance he’ll win the election

  3. More fun election-eve estimates • 22% chance Romney will win in Iowa but Obama will win the national election • 75.7% chance the same party will win both Michigan and Ohio • 48.3% chance Obama gets 300 or more Electoral College votes • 12.3% chance Obama will win between 6 and 8 states that begin with the letter M

  4. More fun election-eve estimates • 22% chance Romney will win in Iowa but Obama will win the national election • 75.7% chance the same party will win both Michigan and Ohio • 48.3% chance Obama gets 300 or more Electoral College votes • 12.3% chance Obama will win between 6 and 8 states that begin with the letter M

  5. Where did you get these numbers? • A: We crowdsourced them • http://PredictWiseQ.com • A fully working beta example of our technical paper in ACM EC’12

  6. The wisdom of crowds

  7. The wisdom of crowds Ignore crowd:if you’re in the99.7th percentile More:http://blog.oddhead.com/2007/01/04/the-wisdom-of-the-probabilitysports-crowd/http://www.overcomingbias.com/2007/02/how_and_when_to.html

  8. Can we do better? • guess • model it - baseline • model it - baseline++ • poll a crowd - mTurk • pay a crowd - probSports contest • pay a crowd - Vegas market • pay a crowd - TradeSports market “Prediction market”

  9. An ExamplePrediction • A random variable, e.g. Will US go into recession in 2013?(Y/N)

  10. An ExamplePredictionMarket • A random variable, e.g. • Turned into a financial instrument payoff = realized value of variable Will US go into recession in 2013?(Y/N) I am entitled to: Recessionin 2013 No Recessionin 2013 $1 if $0 if

  11. 2012 November 28 5:49 a.m. ET

  12. 2012 November 28 5:49 a.m. ET Between 17.3% and 20.7% chance

  13. 11-05-2012 10:09AM http://www.predictwise.com/maps/2012president

  14. Goals for trade Efficiency (gains) Inidiv. rationality Budget balance Revenue Comp. complexity Equilibrium General, Nash, ... Design for Prediction

  15. Goals for trade Efficiency (gains) Inidiv. rationality Budget balance Revenue Comp. complexity Equilibrium General, Nash, ... Goals for prediction Info aggregation 1. Liquidity 2. Expressiveness Bounded budget Indiv. rationality Comp. complexity Equilibrium Rational expectations Design for Prediction Competes with:experts, scoring rules, opinion pools, ML/stats, polls, Delphi

  16. Goals for trade Efficiency (gains) Inidiv. rationality Budget balance Revenue Comp. complexity Equilibrium General, Nash, ... Goals for prediction Info aggregation 1. Liquidity 2. Expressiveness Bounded budget Indiv. rationality Comp. complexity Equilibrium Rational expectations Design for Prediction Competes with:experts, scoring rules, opinion pools, ML/stats, polls, Delphi

  17. Why Liquidity?

  18. Why Liquidity? Low liquidity takes the prediction out of marketshttp://blog.oddhead.com/2010/07/08/why-automated-market-makers/ Between 0.2% and 99.8% chance

  19. Why Expressiveness?

  20. Why Expressiveness?

  21. Why Expressiveness?

  22. Why Expressiveness?

  23. Why Expressiveness?

  24. Why Expressiveness? • Call option and put options are redundant • Range bets require four trades(“butterfly spread”) • Bid to buy call option @strike 15 can’t match with ask to sell @strike 10 • Can’t set own strike • Bottom line: Lacks expressiveness

  25. Why Expressiveness? • Dem Pres, Dem Senate, Dem HouseDem Pres, Dem Senate, GOP HouseDem Pres, GOP Senate, Dem HouseDem Pres, GOP Senate, GOP House... • Dem PresDem HouseDem wins >=270 electoral votesDem wins >=280 electoral votes...

  26. Industry Standard • Ignore relationships:Treat them as independent markets • Las Vegas sports bettingKentucky horseracingWall Street stock optionsHigh Street spread betting

  27. NYSE 1926 http://online.wsj.com/article/SB10001424052748704858404576134372454343538.html

  28. NYSE 1987 http://online.wsj.com/article/SB10001424052748704858404576134372454343538.html

  29. NYSE 2006-2011 • 2011 Deutsche BörseAG • 2007 Euronext • 2006 Archipelago, ipo

  30. NYSE 7pm Sep 10, 2012

  31. New Markets – Same CDA

  32. A Better Way(Or,... Bringing trading into digital age) • Expressiveness • Linear programming • Bossaerts, Fine, Ledyard: Combined Value TradingFortnow et al.: Betting Boolean Style • http://bit.ly/multipm • Expressiveness + Liquidity • Automated market maker • Always quote a price on anything • Downside: requires subsidy/risk

  33. Getting Greedy • Design a marketfor information on exponentially many things • “Combinatorial prediction market”

  34. Combinatorial securities:More information, more fun • Payoff is function of common variables,e.g. 50 states elect Dem or Rep

  35. Combinatorial securities:More information, more fun • Dem will win California

  36. Combinatorial securities:More information, more fun • Dem will lose FL but win election • Dem will win >8 of 10 Northeastern states • Same party will win OH & PA PA OH

  37. Combinatorial securities:More information, more fun • There will be a path of blue from Canada to Mexico WA OR

  38. Some Counting 54 “states”: 48 + DC + Maine (2), Nebraska (3) 254= 18 quadrillion possible outcomes 22541018008915383333485 distinct predictionsMore than a googol, less than a googolplex NOT independent

  39. Overview:Complexity results

  40. A research methodology HSX Design Build Analyze NF TS WSEX FX PS

  41. Prediction markets Dynamic parimutuel Combinatorial bids Combinatorial outcomes Shared scoring rules Linear programming backbone Ad auctions Spam incentives Examples Design Build Analyze • Predictalot • Yoopick • Y!/O Buzz • Centmail • Pictcha • Yootles • Computational complexity • Does money matter? • Equilibrium analysis • Wisdom of crowds: Combining experts • Practical lessons

  42. http://PredictWiseQ.com

  43. http://PredictWiseQ.com

  44. Automated Market Maker • Info propagation Reward traders for information, not computational power

  45. Automated Market Maker • Info propagation Reward traders for information, not computational power

  46. Consistent pricing 1 Independent markets A&B&C 0 0 1 A&B’&C

  47. Consistent pricing 1 Independent markets Prices p A&B&C 0 0 1 A&B’&C

  48. Consistent pricing 1 Independent markets A&B&C 0 0 1 A&B’&C

  49. Consistent pricing 1 Independent markets C = 0.9 A = 0.8 B = 0.6 A&B&C 0 0 1 A&B’&C

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