Prediction MarketsPrediction Markets and and Business ForecastsBusiness Forecasts

Opportunities and Challenges in the New Information EraOpportunities and Challenges in the New Information Era

Professor: Professor: Andrew B. WhinstonAndrew B. Whinston

McCombs School of BusinessMcCombs School of Business

The University of Texas at AustinThe University of Texas at Austin

04/21/2304/21/23

Reference: Fan, Srinivasan, Stallaert and Whinston, “Electronic Commerce and the Revolution in Financial Markets”, Published by Thomson Learning, 2002.

22

A New Way of Making PredictionsA New Way of Making Predictions

2004 Presidential Election 2004 Presidential Election

Winner Takes All MarketWinner Takes All Market

Two stocks traded: Two stocks traded:

REP04REP04: pays $1 per share if : pays $1 per share if

Bush wins, $0 if he losesBush wins, $0 if he loses

DEM04DEM04: pays $1 per share if : pays $1 per share if

Kerry wins, $0 if he losesKerry wins, $0 if he loses

Before Dec 5, 2004, people can Before Dec 5, 2004, people can

freely buy and sell the stocks, freely buy and sell the stocks,

just like the real stock marketjust like the real stock market

The Prices of the stocks: The Prices of the stocks: double auction double auction

mechanismmechanism just like the real stock market just like the real stock market

33

The market price reveals the candidate’s chances of winning

44

Hollywood Stock Exchange (http://www.hsx.com)Hollywood Stock Exchange (http://www.hsx.com)

Movie StocksMovie Stocks

Pays $x per share Pays $x per share

according to the box office according to the box office

income in the first 4 weeksincome in the first 4 weeks

Trade opens when the Trade opens when the

movie starts being movie starts being

plannedplanned

Stock price predicts the Stock price predicts the

box office incomebox office income

55

Types of MarketsTypes of Markets

Other Prediction MarketsOther Prediction Markets

Tradesports (Tradesports (http://www.tradesports.comhttp://www.tradesports.com))

Intrade Intrade ((http://www.intrade.comhttp://www.intrade.com))

Peddypower (Peddypower (http://http://www.peddypower.comwww.peddypower.com))

Economic Derivatives (Economic Derivatives (http://www.economicderivatives.comhttp://www.economicderivatives.com))

NetEchange NetEchange ((http://www.nex.comhttp://www.nex.com))

Foresight Exchange (Foresight Exchange (http://http://www.ideosphere.com/fxwww.ideosphere.com/fx//))

etc.etc.

Subjects:Subjects: Political eventsPolitical events Sports eventsSports events Movies incomesMovies incomes Economic factorsEconomic factors

Interest rateInterest rate Gasoline priceGasoline price Inflation rate, etc.Inflation rate, etc.

New discoveries in scienceNew discoveries in science

Any New Hot Area! Any New Hot Area!

Double Auction(stock market)Double Auction(stock market)

Parimutuel Pricing(betting market)

Parimutuel Pricing(betting market)

One Side Auction(auction market)

One Side Auction(auction market)

66

New Era of Business ForecastingNew Era of Business Forecasting Implementation of the market mechanisms into the Implementation of the market mechanisms into the Decision Support Decision Support

SystemSystem flexibility to integrate new aspects and subjective knowledge in the flexibility to integrate new aspects and subjective knowledge in the

prediction (e.g., a competitor’s unconventional move.)prediction (e.g., a competitor’s unconventional move.)

quantifiable incentives for people to tell the truthquantifiable incentives for people to tell the truth

Fang, Stinchcombe and Whinston (2004)Fang, Stinchcombe and Whinston (2004)

Putting Your Money where Your Mouth IsPutting Your Money where Your Mouth Is

People decide their prediction and how much they want to bet on People decide their prediction and how much they want to bet on

their prediction. their prediction. People will reveal their true predictionPeople will reveal their true prediction

Their bet reveals individual confidence level on the prediction.Their bet reveals individual confidence level on the prediction.

Weights are assigned to individual predictions based on agents’ bets.Weights are assigned to individual predictions based on agents’ bets.

Each person can expect to gain if their information is valuable. The gain Each person can expect to gain if their information is valuable. The gain

increases as the quality of information, which encourage them to learn.increases as the quality of information, which encourage them to learn.

77

1 2 20 0

1 1( , , , ) ~ , : where i ii

n ii i ii i

sX s s s N

A Quick Reminder from StatisticsA Quick Reminder from Statistics

ss11 = = x x + + 11

ss22 = = x x + + 22

……

ssnn = = x x + + nn

How should we estimate X ?

The mean is also an estimator which has the lowest variance among The mean is also an estimator which has the lowest variance among all the linear unbiased estimators (even without normal assumption)all the linear unbiased estimators (even without normal assumption)

2 ~ 0, for 1,2, ,i iN i n

– Normal Learning Theorem (DeGroot, 1971)

Predicting a random factor Predicting a random factor XX ~ ~ NN( 0, ( 0, 0022))

88

The Selection ProblemThe Selection Problem

How would we decide whether the information is too costly?How would we decide whether the information is too costly?

costci

precision i

too expensive

c*()

principal is willing to pay

The cutoff is expected to be an increasing function

99

Selection Problem -- ModelSelection Problem -- ModelA risk neutral firm (the principal) wants to predict a random future state X ~N (0,1)

1 ii S

pv

*ˆ when |1

i ii S

ii S

sX E x

F

If all the agents in the set S share the information (si and ) truthfully with the principal, the “best estimator” is derived from the following maximization problem.

-- a weighted average of signals

1010

The agentsThe agents NN potential potential risk-neutralrisk-neutral agents, each: agents, each:

suffers private cost to access the information, suffers private cost to access the information, cci i ;;

privately knows the precision of their own information source privately knows the precision of their own information source i i ;;

observes private (independent) signal observes private (independent) signal ssii only when they pay the only when they pay the

costs.costs.

((cci i , , i i ) represents the agent’s ex ante type) represents the agent’s ex ante type

QQ((cc,,)) denotes the distribution of agents type, and denotes the distribution of agents type, and qq((cc,,)) is the is the

density; density;

FF(() ) andand ff(()) denotes the marginal distribution and density of denotes the marginal distribution and density of

agent’s precision;agent’s precision;

HH((cc)) and and hh(c)(c) denotes the marginal distribution and density of denotes the marginal distribution and density of

agent’s costs.agent’s costs.

1111

Benchmark cases when precision is verifiableBenchmark cases when precision is verifiable-finding optimal -finding optimal c*(c*())

The principal sets The principal sets c*(c*() ) Agents with precision Agents with precision ii decides whether to decides whether to

participateparticipate Auditable costsAuditable costs: the principal can audit the cost the : the principal can audit the cost the

agents spend and reimburses the agents up to agents spend and reimburses the agents up to c*c*auau(().). Non-auditable costsNon-auditable costs: the principal can not audit the : the principal can not audit the

cost hence pays the agents cost hence pays the agents c*c*nonnon(()) Inside the firm: the principal needs to take into account the Inside the firm: the principal needs to take into account the

fact that the agents consumes resources inside the firm to fact that the agents consumes resources inside the firm to get the prediction.get the prediction.

The set of agents who will participateThe set of agents who will participate

1212

Mathematic treatmentMathematic treatment

Auditable cost: Non-auditable cost:

*

*1

*

*

2

: The principal's expected payoff from the prediction

by collecting information from the set of agents un

*

* *

de

1

r

0

.

2

,

max

,1 1

1

N

i

i

audit

c

i ii c

c

i

c

i

c

c c

pv dQ c

c

c

R

*2

*2

*

: The principal's expected compensation

paid to the agents un

0

der .

,,N

i

i

ic

c

c

c dQ c

R

*

*

2

1

*

*

: The principal's expected payoff from the prediction

by collecting information from the set of agents u

*

* *1

nd

2

0,

er .

max

,1 1

i

N

i

non audit

c

i ii

c

c

c

c

c c

pv dQ c

c

c

R

*2

*

*2

: The principal's expected compensation

paid to the agents under .

,

0

* 1 ,

i

Ni

ici

c

c

ic dQ c

R

1313

Results of Existence and MonotonicityResults of Existence and Monotonicity

Assumptions: Assumptions: The density q is greater than 0 on a set of the The density q is greater than 0 on a set of the

form for form for

some non-decreasing function some non-decreasing function

and some and some

Proposition:Proposition: In both cases, we can find the optimal c* In both cases, we can find the optimal c*

maximizes the principal’s payoff; moreover, c* maximizes the principal’s payoff; moreover, c* is non-decreasing.is non-decreasing.

1, , : ,0N N

i iS c R a T i I c f

: 0,f R

0 .a T

1414

Result (cont)Result (cont)

Non-auditable case:

c* will always satisfy c* will always satisfy c*(c*() has to be zero even as long as there exists some agent with ) has to be zero even as long as there exists some agent with precision precision ..

Auditable case:

c* is set so that no agent with strictly positive cost will be selected. c*(c*()) need not be zero if the principal believes that there is no agent with precision and strictly positive cost.

*, :lim 0 for all 0.i i N i iN

c c cQ

* *lim 0 for a: ll 0| >i N i N i iN

HQ c c

Generally speaking, we can get that c* goes to zero when the number of agents goes to infinity.

* * | 0N i N i ic H c

1515

Betting mechanism designBetting mechanism design

The principal asks agents to report their own predictionThe principal asks agents to report their own prediction

((rrii)) and to decide how much they want to bet on their and to decide how much they want to bet on their

prediction prediction ((BBii)). .

Each agent gets rewarded after the state Each agent gets rewarded after the state xx is observed. is observed.

The reward functionThe reward function f f = 2= 2BBii1/2 1/2 ( ( a a - - bb((rrii--xx))2 2 ) )

where where aa 0, 0, bb 0, are parameters set by the firm. 0, are parameters set by the firm.

Each agent’s optimal strategy (Each agent’s optimal strategy (rrii**((ssii, , ii), ), BBii

**((ssii, , ii) ) is ) ) is

derived by solving the following problemderived by solving the following problem ,

max | , |, , ,i i

i i ii i i i ir B

f BE s E sr x B

1616

PropositionProposition:: (optimal strategy) (optimal strategy)

2

*

*

2

-- increasing function;

agents bet more if they have better information;1

-- agents report their private expectation of 1

-- agen

( | , )1

ii

i ii

i

i i ii

bB a

sr X

bE s a

ts get positive profit if their precision is

accurate enough. They get more if their precision

is higher.

1717

RevelationRevelation

Corollary: (revealing)Corollary: (revealing)

12

12

*

*

*

*

1

for 0 i.e. 1

i

i

i

i

i

i

i

b

a bB

b a

b a

B

rsB

The signal and precision are reflected through the bet and report.

1818

, :1i

i

bS a b i c a

PropositionProposition:: (participation) (participation)

PropositionProposition:: (optimal parameters) (optimal parameters)

When When p p > 0, > 0, bb** aa** > 0 when > 0 when hh((cc) is continuous and ) is continuous and hh(0) >0(0) >0

People will participate when their cost of acquiring the signal islower than the gain from the betting market.

The optimal reward function always exists. It varies when the principal’s perceived distribution functions of cost and precision change.

1919

Discussion of Simultaneous Betting MarketDiscussion of Simultaneous Betting Market

Repeated BettingRepeated Betting due to anonymity. due to anonymity.

If an agent can acquire two identities and bet twice, she If an agent can acquire two identities and bet twice, she

will repeat the optimal strategy twice and get twice as will repeat the optimal strategy twice and get twice as

much her expected payoff. much her expected payoff.

The predictor is less efficient (i.e. variance is larger)The predictor is less efficient (i.e. variance is larger)

The loss of efficiency is the largest when The loss of efficiency is the largest when

Possible ex post Inefficiency: Possible ex post Inefficiency:

the principal may regret setting a parameter too high or the principal may regret setting a parameter too high or

too low after observing the agents’ participation.too low after observing the agents’ participation.

Example: two extreme cases of Example: two extreme cases of

5 1

4a a

a b

2020

DynamicsDynamics Principal’s trade-off: whether should I stop learning now?Principal’s trade-off: whether should I stop learning now?

To generate forecast earlier (time discount)To generate forecast earlier (time discount) Pay more, improve forecast, but decide latePay more, improve forecast, but decide late

Dynamic Programming:Dynamic Programming:

min : t tt

pT t V v

Optimal Stopping Time

(1) when 1, decreases as decreasesT N

* *(2) ( 1)seq simultE E

Intuition: ability to adjust the parameter according to how information is incorporated

2

1 1 11

,max ,max

1tt t

tt t t t t

tta b

t

p bV v E V a

2

11

,max ,max

1tt t

tt t t

tta b

t

p bv E V a

1t

pv

,

max,t ta b

2

1

1t

tt t t

tt

bE V a

2

1

tt

t

ba

1t t

tV

2121

ExtensionExtension

Extension: auctions marketExtension: auctions market

Implications to the new organization formsImplications to the new organization forms

Q&AQ&A

T h a n k Y o u !T h a n k Y o u !