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Transcript of Prediction Markets and Business Forecasts Opportunities and Challenges in the New Information Era...
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 !