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 Disneys 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

Bush Clinton Other
Prices .50 .40 .10
U think .3 .7 0

• You see a way to make some money.

10
How the IEM might work.
Bush Clinton Other Cash E(V)
Prices .50 .40 .10
U Think .3 .7 0
U buy 1 1 1 -1 1-1 0
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How the IEM might work.
Bush Clinton Other Cash E(V)
Prices .50 .40 .10
U Think .3 .7 0
U buy 1 1 1 -1 1-1 0
U trade -1 _at_ .35 1 _at_ .50 -1 _at_ .05 -.10
12
How the IEM might work.
Bush Clinton Other Cash E(V)
Prices .50 .40 .10
U Think .3 .7 0
U buy 1 1 1 -1 1-1 0
U trade -1 _at_ .35 1 _at_ .50 -1 _at_ .05 -.10
U have 0 2 0 -1.10 1.40-1.10
You actually will make (0.38x2) - 1.10 -0.34.
But you dont know that when you make this
transaction. You can only act on your beliefs.
13
How the IEM might work.
Bush Clinton Other Cash E(V)
Prices .50 .40 .10
U Think .3 .7 0
U buy 1 1 1 -1 1-1 0
U trade -1 _at_ .35 1 _at_ .50 -1 _at_ .05 -.10
U have 0 2 0 -1.10 1.40-1.10

• 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
1992 U.S. Election
Source IEM (2005)
15
How Accurate Has IEM Been?
Source IEM (2005)
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 Cant 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 dont see that.
• I see and you dont 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 dont 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 Maxwells Demon
24
Why might an IM not work?

• Lets 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 occurring IMs
• 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 DataGrus 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
Pari-Mutuel Market
Got it 41 63
Got it means KL lt .01 or p-FI lt .05
When N gt 6, the market gets it 80 and the
pari-mutuel gets it 75.
39
Summary Statistics32 observations for PM, M, P
Pari-Mutuel Market
Got it 30 (75) 55 (80)
Early 0 38
N 3, 12
Early means in 1st 3 transactions. Not in time.
40
Summary Statistics32 observations for PM, M, P
Pari-Mutuel Market
Got it 30 (75) 55 (80)
Early 0 38
Mirages 25 22
Mirage means p is not the FI and is one of the
other possibilities.
41
Summary Statistics32 observations for PM, M, P
Pari-Mutuel Market
Got it 30 (75) 55 (80)
Early 0 38
Mirages 25 22
tickets or transactions per subject N 3, rest 2.5, 7.8 N 3, rest 1.6, 6.2
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 IMs 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 USaid 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 2320 2 1096 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 IMs.
• 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?
51
Better but Still not Great
PM PM/S M M/S
Got it 41 31 63 66
Early 0 3 47 56
Mirages 25 13 22 13
Tickets or actions 4.8 13.8 3.8 5.4
52
Design New Mechanisms

• With one agent, a Scoring Rule is a good
  mechanism to elicit beliefs.
• Report r. Receive Sln(r/2) in asset that pays
  1 if A and Sln((1-r)/2) in asset that pays 1
  if B.
• Incentive compatible to report true beliefs
• Encourages participation
• Provides an expected value greater than 0.
• Brier (1950) Monthly Weather Review, Goode
  (1952), Savage (1971) JASA, Page (1988)(PSR ?
  VCG)
• Lets adapt this to multi-agent situations.

53
If it Works for One Person

• Market Scoring Rules may be good mechanisms.
• Hanson (2003)
• An automated market maker (MM)
• Any trader can access the MM, at any time and
  trade assets according to a scoring rule by
  announcing his belief.
• The scoring rule is seeded with the last traders
  announcement of their beliefs.
• Each new announced belief is publicly reported.
• Incentive compatible to report true beliefs
  (somewhat)
• At one iteration, but not over all iterations.
• Possible to mislead early and gain later
  (particularly if N 3)
• Encourages participation (somewhat)
• Positive expected value to the group.

54
An Old Standby Dressed Up

• A Poll with Incentives may be a good mechanism.
• Basic design is standard.
• All are polled and asked their beliefs.
• Beliefs are averaged and publicly announced.
• Repeated m times (We did 5 and 3.)
• But at the end, each agent is paid according to
  the same scoring rule.
• Incentive compatible to report true beliefs
  (somewhat)
• True at equilibrium if there is
  full-information aggregation
• Open question whether it is true during
  iterations
• Encourages participation
• Positive expected value to everyone in the group.

55
Pretty much the same.
ave KL PMS .042 MSR .045 P .047 MS .
051
kl(.8,.65).06 kl(.8,.50).22 kl(.8,.20).83
56
P and MRS get it (always) gtgt MS and PMS
ave KL Mirage MSR .000 0 P .004
0 PM .013 0 PMS .061 0 MS .085 2 M .100
2
kl(.8,.65).06 kl(.8,.50).22 kl(.8,.20).83
57
Summary Statistics32 observations (all N)
P MSR MS PMS
Got it 53 75 66 31
Early 22 56 47 3
Mirages 6 6 13 13
KL dist. .025 .023 .068 .051

• In MSR, first mover wins. In Pari-mutuel,
  last mover wins.
• In time lapsed, MSR hits it really fast.

58
RepriseDo traditional IMs work?

• YES Large numbers of informationally small
  agents and reasonably simple environments seem to
  overcome some of the no-trade incentives in
  traditional markets and pari-mutuels.
• I dont think we yet know exactly why. (Open
  Puzzle!)
• NO With informationally large agents, much less
  incomplete markets or complex decision problems,
  it does not look so good.
• N 3 creates serious problems for both markets
  and pari-mutuels, even in simple environments.
• More research is needed here.

59
Reprise Can we design IMs that work?

• YES For informationally small agents in simple
  environments,
• The Market Scoring Rule gets it early and often.
• Polling with incentive payments also works pretty
  well but is slower to get the job done.
• Markets are mirage prone, even with noise
  traders.
• Pari-mutuels are slow, even with subsidization
• MAYBE For informationally large agents,
• The four best (ms, msr, p, pms) are all off by.10
  to .15.
• All mechanisms we looked at can be improved upon.
• Or is there an impossibility theorem? (Open
  Puzzle!)

60
The End

• I leave you with two questions that I believe are
  worth pursuing.

61
?
Is

Market Maker Maxwells Demon
Is the best mechanism?
MSR