Information Markets

1. Information Markets John Ledyard April 13, 2005 Nancy Schwartz Memorial Lecture KGSM, Northwestern University

2. What would you like to know? • What will Disney’s profits be in 2006? • Ask an accountant, a stock analyst, a consultant, the CEO, Mickey Mouse, … • Who will the next Pope be? • Ask a pundit, a cardinal, take a poll, …… • How stable will the middle-east be on 12/31/05? • Ask the CIA, the Mossad, the Defense Department, the President, a committee of experts, ……. • Should you set up an Information Market?

3. What is an Information Market? • This is not about markets for information. • Kihlstrom (1974), Radner and Stiglitz (1984), Kamien and Tauman (1990), Keppo, Moscarini, Smith (2005) • It is about using market forces to bring together disparate bits and pieces of information and add them up, or aggregate them, for use in predictions or decisions. • Google hits • Information Markets = 25,700,000 • Prediction Markets = 1,550,000

4. How would it work? • Familiar Question: Who will win an election? • Standard approach - Polls. • In 1988, University of Iowa Business School securitized the Presidential election prediction on the internet.

5. The Iowa Election Market • In 1992, for $1.00, Iowa sold or bought a set of securities that covered all possible outcomes of the election; Bush, Clinton, Other (included Perot).

6. The Iowa Election Market • In 1992, for $1.00, Iowa sold or bought a set of securities that covered all possible outcomes of the election; Bush, Clinton, Other (included Perot). • Each security paid $1 times the percentage of the vote for that person. Securities were traded.

7. The Iowa Election Market • In 1992, for $1.00, Iowa sold or bought a set of securities that covered all possible outcomes of the election; Bush, Clinton, Other (included Perot). • Each security paid $1 times the percentage of the vote for that person. Securities were traded. • After the election tally, if you owned 100 shares of Bush and Bush received 38% of the vote then you would be paid $38.

8. The Iowa Election Market • In 1992, for $1.00, Iowa sold or bought a set of securities that covered all possible outcomes of the election; Bush, Clinton, Other (included Perot). • Each security paid $1 times the percentage of the vote for that person. Securities were traded. • After the election tally, if you owned 100 shares of Bush and Bush received 38% of the vote then you would be paid $38. • The actual result was Clinton 43%, Bush 38%, Perot 19%

9. How the IEM might work. • You go to the IEM website and see • You see a way to make some money.

10. How the IEM might work.

11. How the IEM might work.

12. How the IEM might work. You actually will make (0.38x2) - 1.10 = -$0.34. But you don’t know that when you make this transaction. You can only act on your beliefs.

13. How the IEM might work. • Other traders then adjust their beliefs in response to the price changes. And so on. • If all goes well, in equilibrium, prices will equate to the full-information beliefs of the traders. • And if all goes well, these will be the true vote-shares.

14. Source: IEM (2005) 1992 U.S. Election

15. Source: IEM (2005) How Accurate Has IEM Been?

16. Also….. • National election market in NY (1868-1940) • [Rhode and Strumpf (2004)] • “Over $165 million (in 2002 dollars) was wagered in one election, and betting activity at times dominated transactions in the stock exchanges on Wall Street.” • “In only one case did the candidate clearly favored in the betting a month before Election Day lose.”

17. Is this a Free Lunch? • Iowa pays nothing. • On average, the traders earn nothing • But, in the end, everyone is better, maybe even maximally, informed.

18. “The Next Killer App”? or “Too Good To Be True”? • Evidence, mostly empirical, suggests Information Markets Work. • Evidence, mostly theoretical, suggests Information Markets Can’t Work. • Today we will explore • how “Information Markets” work • how to design and engineer viable and accurate “Information Mechanisms”

19. Why might an IM work? • There are two of us in this scenario. • (Neither of us is a Game Theorist.) • There are 2 coins: • Coin A comes up heads 80% of the time. • Coin B comes up heads 20% of the time. • One is chosen with probability .5. • This is our common prior. • The coin is flipped twice for each of us. • You see (H,T) and I don’t see that. • I see and you don’t see that.

20. Why might an IM work? • Remember: Coin A = .8 heads, Coin B = .2 heads, you see (H,T), I see (?, ?). • What is the probability that the coin is A? • Based on only your information, the answer is 0.5. • This is your initial posterior. • Suppose there is a Market Maker who posts prices and asks us whether we want to buy or sell an asset that pays $1 if the coin is A and $0 if it is B. • He posts a price of 0.60. • You offer to sell and I offer to buy.

21. Why might an IM work? • Remember: Coin A = .8 heads, Coin B = .2 heads, you see (H,T), I see (?, ?), I offered to buy at .6. • What is the probability that the coin is A? • Since you know that I must have seen (H,H), you know (H,T,H,H). This is everything. • Your answer should be 0.94. • Of course, I only know that you are either (H,T) or (T,T), so I don’t know everything - yet.

22. Why might an IM work? • Suppose the Market Maker still posts a price of .6. • We both offer to buy. • I now know that your current posterior is .94 which means you must have seen (H,T) • So we both now know that the total information is (3H, 1T) and our posteriors are the same: 0.94. • The “market” has “aggregated” the “information”! • The underlying theories are Rational Expectations Equilibrium and Common Knowledge Information. • Green (1973), Lucas (1972), Grossman (1977) • Aumann (1976), Geanakopolos and Polemarchakis (1982)

23. But Wait!!!! There is something fishy here! ? = Market Maker Maxwell’s Demon

24. Why might an IM not work? • Let’s go back to the Market and get rid of the Market Maker. • Remember: Coin A = .8 heads, Coin B = .2 heads, you see (H,T), I see (?, ?), the asset pays $1 if A. • I offer to sell you 2 units of the asset for .30. • What should you do now? • Infer that I saw (T,T) and believe (1 H, 3T). • So you now should believe that P(A) = .06

25. Why might an IM not work? • I offer you 2 units of the asset for .30, you saw (H,T) and know I saw (T,T), so your P(A) = .06. • You believe the expected value of the asset is .06. • Obviously you should reject my offer. • The full information is either (1H,3T) or (0H,4T). • If you had seen (H,H) you would accept my offer. • If you bid to buy above .004, I also know it is 0.6. • We will not trade! • The underlying theory is No-Trade Theorems • [Grossman and Stiglitz (1976), Milgrom-Stokey (1988)]

26. What About Empirical Evidence? • There are many naturally occurringIM’s • And, in direct comparisons, they beat other institutions.

27. Pari-mutuel betting

28. Pari-mutuel betting • Racetrack odds beat track experts • Figlewski (1979)

29. Futures markets

30. Futures markets • OJ futures improve freeze forecasts • Roll (1984)

31. Stock markets

32. Stock markets • Stock prices beat the experts panel in the post-Challenger probe • Maloney & Mulherin (2003)

33. Less Positive Field Evidence • The consensus forecast (median of about 30 economists) has as much predictive power as the Goldman-Sachs pari-mutual market. • [Wolfers and Zieztwitz (2003)] • Wide bid-ask spreads and thin trading on most Tradesports.com markets. • Politics (4/11/05) (contract, price, spread, vol.) • 2008DemnomClinton 40 1.5 9135 • 2008 RepnomJBush 10 .2 2685 • Papacy (4/11/05) (contract, price, spread, vol.) • Italy 42 .9 2045 • Nigeria 13 1.7 1454 • USA 0.2 .5 274

34. The Experimental Evidenceis Mixed • A number of experimentalists have demonstrated convergence to the full information rational expectations equilibrium. • In laboratory asset markets with one asset • Forsythe, Palfrey, Plott (1982) • In laboratory elections • McKelvey & Ordeshook (1985) • In laboratory asset markets with 3 assets • Plott and Sunder (1988)

35. The Experimental Evidenceis Mixed • A number of experimentalists have demonstrated that information mechanisms do not always work. • In laboratory asset markets, if preferences differ and there are incomplete markets, there is little aggregation. • Plott and Sunder (1988) Risk or ambiguity aversion? • In iterative polls in the laboratory, there is incomplete information aggregation. • McKelvey & Page (1990) Incomplete Bayesian updating? • In laboratory pari-mutuel betting, we observe mirages. • Plott (2002) (Pari-mutuel) Information cascades?

36. One More Set of Data[Grus and Ledyard (2005)] • The 2 coin example, 2 flips each • N = 3, 7, 8, 12: Caltech subjects • Market, Pari-mutuel • 3 minutes of transactions per period • 8 periods per mechanism • 3 mechanisms per session (2.5 hours) • Earnings approximate $33/subject

37. Numbers Matter! These are big mirages. MP informational size = .58 for N = 3 = .20 for N = 7 = .02 for N = 12 kl(.8,.65)=.06 kl(.8,.50)=.22 kl(.8,.20)=.83 These get it!

38. Summary Statistics32 observations “Got it” means KL < .01 or | p-FI | < .05 When N > 6, the market “gets it” 80% and the pari-mutuel gets it 75%.

39. Summary Statistics32 observations for PM, M, P N= 3, 12 Early means in 1st 3 transactions. Not in time.

40. Summary Statistics32 observations for PM, M, P Mirage means p is not the FI and is one of the other possibilities.

41. Summary Statistics32 observations for PM, M, P

42. Based on the 2-coin experiments(and more complicated ones) • Some aggregation occurs but it is not perfect. • Markets are faster than pari-mutuels and get it more often. • Both are subject to mirages. • Neither perform well at low-scale (N = 3). • There is evidence to support the no-trade hypothesis, particularly when N = 3. • But there is still some trading. • Incomplete updating? Not here. • Boredom - yes, lots of little trades • Greater fool? - Possibly.

43. Summary to here • There is theoretical, experimental, and field evidence that traditional IM’s may work. • But there is also evidence that there are impediments to complete information aggregation especially in environments with informationally large agents. • Should we worry about small numbers? • Can we find better information mechanisms?

44. Numbers and Informationally Large Traders • Probability of success in next year for drug A? • Expected sales of SUV model X in 2006 contingent on gas prices above $5 on July 2006? • The expected software shipping date contingent on retaining feature R? • Expected benefits of a government program conditional on one of several possible actions? (better cost-benefit analysis?)

45. Remember PAM? • 8 nations, 5 indices, • 4 quarters • Political stability • Military activity • Economic growth • US $ aid • US military activity • Up, Down, or Constant • Implies 320 active markets. • Example contract: Jordan is more politically stable in 4Q2005 conditional on US military activity down in Iraq in 3Q2005 and US$aid in 2Q2005 up in Iran.

46. Remember PAM? • 8 nations, 5 indices, • 4 quarters • Political stability • Military activity • Economic growth • US $ aid • US military activity • Up, Down, or Constant • Implies 320 active markets. • 320 questions and completeness • implies 2^320 = 2 * 10^96 contracts.

47. Need Better Information Mechanisms • To be useful in many potential applications, Information Markets need to perform well with small numbers and informationally large traders. • Traditional markets and pari-mutuels are not up to this. • Two possible approaches • Subsidize the action in the traditional designs. • Design new mechanisms.

48. Better Information Mechanisms? • Let us first try to subsidize and modify the traditional IM’s. • Pari-mutuel: Add some tickets into the pot so that the expected payoff of spending $1 is larger than $1. • Market: Randomly accept bids and offers at “market.” • Noise trading [Grossman and Stiglitz (1976)]

49. Helps when N = 3 kl(.8,.65)=.06 kl(.8,.50)=.22 kl(.8,.20)=.83

50. Helps when N = 3 kl(.8,.65)=.06 kl(.8,.50)=.22 kl(.8,.20)=.83 Does this mean “Noise Creates Information”?