Information Markets II: Theory,
Outputs, Inputs, Foul Play,
Combinatorics, Applications
Robin Hanson
Economics
George Mason University
Theory I - Old
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No info - Supply and Demand
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Assume beliefs not respond to prices
Price is weighted average of beliefs
More influence: risk takers, rich
Info, Static - Rational Expectations
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Price clears, but beliefs depend on price
No trade if not expect “noise traders”
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Price not reveal all info
More influence: info holders
Theory II - Market Microstruture
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Info, Dynamic – Game Theory
Example – Kyle ’85
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X - Informed trader(s) – risk averse
Y - Noise trader – fool or liquidity pref
Market makers – no info, deep pockets
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If many compete, Price = E[value|x+y]
Info markets – use risk-neutral limit
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If Y larger, X larger to compensate
more info gathered, so more accuracy!
Theory III – Behavioral Finance
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Humans are overconfident
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Far more speculative trade than need
Mere fact of disagreement shows
Overconfidence varies with person,
experience, consequence severity
Implications
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Price in part an ave of beliefs?
Adds noise to price aggregates?
Prices more honest than talk, polls, …
Outputs
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What price is best estimate?
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Require post comment with each trade?
Use trade record in performance review?
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last? median? an average? Reweight trades?
If not last, auto-trader to fix makes $!
 This good discipline re if really can fix
 Imagine Govt agency fixing stock prices!
Reward contribution vs. infer other abilities
Crunch trade data to see who thinks what
Give more a feeling of participation?
Don’t let these issues distract you from:
Ask the Right Questions
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High value to more accurate estimates!
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Where suspect more accuracy is possible
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Suspect info is withheld, or not sure who has it
Prefer fun, easy to explain and judge
Can let many know best estimates
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Relevant standard: beat existing institutions
Not fear estimates reveal secrets
Not using uncertainty, biases to motivate
Avoid inducing foul play
Conditional Estimates
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Can avoid self-defeating predictions
Condition on decision, advises it
Don’t confuse correlation and cause
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Bias if decision makers will know more
Clear decision time and use prices then
Choose instrumental variables
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E.g., condition on random decision
Inputs I
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Final Judging – using prices risks gaming!
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Refine claim – central vs. decentralized
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Audit lotteries reduce ave cost, but more risk
Credentialing as compromise?
Participants
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Mainly want people can get relevant info
 Diversity helps, but only of info
Trading experience a plus, but not the key
Standard trading needs min traders/claim
Fools are fine, up to a point
Inputs II
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Cash, play money, or prizes to best traders?
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Real Choice: stuff vs. brag rights vs. fun
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Fun risks them not caring enough to be honest
Scale economies of bragging rights?
“Info $” concept: brag of $ value of info add to org
How much must pay?
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Recent paper: on football, real vs. play-prizes same
Note: prizes risk inducing large random trades!
If many have info, just need induce them to tell
If traders must do research, must be paid more
Bigger trader pool helps find low cost providers
When pay: cash upfront, per trade, market maker
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Subsidized market maker pays only for new info
Foul Play I
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Generic fix: limit who/when trade
Lying
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If advisors can bet, may talk less
Fix?: Let advisors show bet stake
Manipulation
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Idea: lose on trades, gain in decisions
Field: Effect rare, short-lived
Lab: no net effect? (see conf talks)
Theory: trading on any consideration other
than asset value is noise trading
Foul Play II
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Sabotage (Moral Hazard)
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Embezzlement –
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Rare (Not 9/11, ’82 Tylenol, ’02 PaineWebber)
Hard match willing capital & skilled labor
Fix: Avoid thick market on small events
Fix: Bound individual stakes (eg finish project)
Stat insiders windfall? Keep info from team?
Fix: Special accounts trade first
Fix?: new color of $, subsidy at info value est.
Retribution – anonymity helps at a cost
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Can still brag re overall record
Combinatorics I – The problem
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Each trader wants to trade on his info, be
insured against all other issues
Ex: what weather can we forecast?
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Old story:
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Per hour per zip code?
Distribution over wind, rain amount?
Conditional on recent, nearby weather?
Vast # possible Arrow-Debreu assets
But fixed costs, traders avoid thin
But regulation is biggest cost by far
Many computing tricks not tried
Combinatorics II - Approaches
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All: decompose trades into state assets
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Call markets
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Example: Win, place, show overlaps
Compute to find matches in offer pool
Related markets thicken each other
Recent computational complexity results
Market makers
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Stands ready to trade all assets
Requires subsidy per base claim, but not for
adding all combos of base
Open issues re combinatorial explosion
Accuracy
Pushing the Limit
Simple Info Markets
Market Scoring
Rules
Scoring
Rules
opinion
pool
problem
thin market
problem
.001
.01
.1
1
Estimates per trader
10
100
pi n
ion
P
du
al
1.400
0.100
0.050
0.800
0.000
0.600
oo
Do
l
ub
le
Au
c ti
Co
on
mb
i ne
dV
alu
e
Ma
rk e
tM
ak
er
0.250
pi n
ion
P
0.150
du
al
1.600
Lo
gO
0.300
KL Distance
0.200
Ind
i vi
Do
oo
l
ub
le
Au
c ti
Co
on
mb
i ne
dV
alu
Ma
e
rk e
tM
ak
er
Lo
gO
Ind
i vi
KL Distance
Accuracy (95% C.L.)
3 Variables
8 Variables
1.200
1.000
Applications
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Private Policy
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Public Policy
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Sales (own and others)
Project completion, quality (bug rate)
Decisions: mergers, subcontractor
choice, regional expansions, …
Epidemics,
monetary policy, health policy, ...
School & job applicants …