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Decision Making under
Uncertainty
서경원
2014 조락교 신진경제학상 강연
Probability
• Probability is widely accepted and used in physics, statistics, economics
and so on
• No one can observe/verify probability
 A coin turns up head with probability 1/2
 Frequentist’s view: out of an infinite number of coin tosses, exactly
half of them turn head
 Not observable
• Probability is an assumption rather than a result
• Today, I will discuss cases where probability is not enough for modeling
uncertainty in economics
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Uncertainty
• Uncertainty = Risk + Ambiguity
 Risk: probabilities are known
 Ambiguity: probabilities are unknown (or unknown risk)
• sometimes referred to as Knightian uncertainty
• Frank Knight (1921)
“[…] a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is
so far different from an unmeasurable one […]”
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Ellsberg Paradox
?
?
10 balls
…
…
# of blue balls
is unknown
10 balls
# of black balls is 5
• Choose one:
 1) between bet on blue vs. bet on black
 2) between bet on yellow vs. bet on white
• Typical choice: 1) black 2) white
• Probability model can’t explain the choices
 1) black: prob(blue)<50%
 2) white: prob(yellow)<50%
 prob(blue or yellow) is less than 100%
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• Probability is not enough to model the choice
• Real world example – stock markets
 The box may be viewed as a firm
• Blue: new product, innovation, cost reduction, …
• Yellow: failure to invent a new product, cost increases, …
 Bet on green: buying the stock
 Bet on red: selling the stock
 Blue-yellow box: more ambiguity in the firm
• small firms, new firms, venture firms …
 Black-white box: less ambiguity (or no ambiguity) in the firm
• big firms, old firms, …
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Model of Ambiguity: Multiple Priors
• Multiple priors: Gilboa and Schmeidler (1989)
 Instead of a single probability, an agent considers a set of probabilities
 When betting on blue, 3 blue balls
 When betting on yellow, 7 blue balls
10 balls
…
10 balls
10 balls
or
…
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Model of Ambiguity: Probability over Probabilities
• Probability over probabilities: Segal (1987), Klibanoff, Marinacci and
Mukerji (2005), Ergin and Gul (2004), Nau (2006), Seo (2009)
 3 blue balls with probability ½
 7 blue balls with probability ½
10 balls
with probability 1/2
10 balls
…
…
10 balls
with probability 1/2
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Financial Market Participation
• Consider a stock market and an investor
 The current stock price is 2000
 The investor has a belief on the price from a month now
 The future price is expected to be higher than, lower than or exactly
equal to 2000
• Future price expected to be >2000: buy the asset (long position)
• Future price expected to be <2000: sell the asset (short position)
• Future price expected to be exactly 2000: do nothing (neutral position)
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Effect of Risk
• Does risk (or risk aversion) change the behavior?
 When buying, buy less
 When selling, sell less
 When doing nothing, doing nothing
• Except the knife-edge case, people should participate in stock markets
(and bond markets as well)
 Not true in the real world
 (Transaction cost can’t explain this for wealthy people (VissingJorgenson (2003)))
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Effect of Ambiguity
• People do not participate in stock markets if she feels ambiguity and
behaves pessimistically:
 if I buy, price is expected to drop
 if I sell, price is expected to rise
• Effect of ambiguity is qualitatively different from effect of risk
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• Mukerji & Tallon (2001): ambiguity generates incomplete markets
• Caballero & Krishnamurthy (2008), Caballero& Simsek (2012): market
freeze under ambiguity in financial crises
• Condie & Ganguli (2009): private information may not be fully revealing
due to ambiguity
• Trojani & Vanini (2004): ambiguity averse group might have no effect on
the asset price
• Condie (2010): ambiguity averse agents affect prices
• Easley & O'hara (2011): market design reducing ambiguity to promote
participation
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Statistical Decision Making under Uncertainty
• Observe a series of observations. Make decisions regarding future
realizations
 For example, collect and analyze economic data, and choose an
economic policy
• Does the above procedure make sense under risk?
 Yes: De Finetti Theorem
 If ordering of a dataset does not matter, statistical procedure makes
sense
 Probabilities are assumed
• Does the above procedure make sense under ambiguity?
 Yes: Epstein and Seo (2010, 2014), Klibanoff, Mukerji and Seo (2013),
Al-Najjar and De Castro (2014)
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