Transcript Prospect Theory - Warsaw School of Economics

Prospect Theory
23A i 23B, reference point
23A) Your country is plagued with an
outbreak of an exotic Asian disease,
which may kill 600 people. You are
responsible for making decision
about two programs. Which program
will you choose:
23B) Your country is plagued with an
outbreak of an exotic Asian disease,
which may kill 600 people. You are
responsible for making decision
about two programs. Which program
will you choose:
a)
a)
b)
Program A: 200 people will be
saved for sure
Program B: 600 will be saved with
probability 1/3, nobody will be
saved with probability 2/3.
b)
Program A: 400 people will die for
sure
Program B: Nobody will die with
probability 1/3, 600 people will die
with probability 2/3.
Kahneman, Tversky (1979) [framing, Asian disease]
Lotteries in 23A) are exactly the same as lotteries in 23B).
Framing is different though.
People often:
• Choose program A in 23A
• Choose program B in 23B
Gains and losses
• Which lottery would you choose
– A) sure gain of $ 3 000
– B) 1:3 chance of getting $ 4 000 or nothing
• Which lottery would you choose
– X) sure loss of $ 3 000
– Y) 3:1 chance of losing $ 4 000 or nothing
5
Conclusion 1
• What matters is not final position, but
changes relative to some reference point
(status quo)
• Depending on the reference point a given
consequence may be interpreted as gain or
loss (framing)
• People are
– Risk prone in the domain of losses
– Risk averse in the domain of gains
20.1 i 20.2 (or how we perceive
probabilities)
20.1) There is 90 balls in the urn – 30 blue balls and 60 that are either yellow or red.
You pick a colour. Then one ball is drawn randomly from the urn. If the colour of the
ball drawn and the colour of the ball you chose match, you will win $100. Which
coloor do you pick? (One answer)
a)
b)
Blue
Yellow
20.2) Continuation: If the colour of the drawn ball is of one the colours you bet on,
you win $100. Which colours do you pick? (One answer)
a)
b)
Blue and Red
Yellow and Red
Ellsberg paradox (1962?) [uncertainty aversion]
Many people choose:
• Blue in 20.1
• Yellow and Red in 20.2
Why is it strange…
17.1 i 17.2 (or how we perceive
objective probabilities)
17.1) Choose one lottery:
P=(1 mln, 1)
Q=(5 mln, 0.1; 1 mln, 0.89; 0 mln, 0.01)
17.2) Choose one lottery:
P’=(1 mln, 0.11; 0 mln, 0.89)
Q’=(5 mln, 0.1; 0 mln, 0.9)
•
•
•
•
•
P better than Q
U(1)>0.1*U(5)+0.89*U(1)+0.01*U(0)
Substitute for U(0)=0 and rearrange:
0.11*U(1)>0.1*U(5)
Hence P’ better than Q’
Kahneman, Tversky (1979) [common consequence effect
violation of independence]
Many people choose P over Q and Q’ over P’
18.1 i 18.2 (or how we perceive
objective probabilities)
18.1) Choose one lottery:
P=(3000 PLN, 1)
Q=(4000 PLN, 0.8; 0 PLN, 0.2)
18.2) Choose one lottery:
P’=(3000 PLN, 0.25; 0 PLN, 0.75)
Q’=(4000 PLN, 0.2; 0 PLN, 0.8)
•
•
•
•
•
P better than Q
U(3)>0.8*U(4)+0.2*U(0)
Divide by 4 and substitute for U(0)=0:
0.25*U(3)>0.2*U(4)
Hence P’ better than Q’
Kahneman, Tversky (1979) [common ratio effect, violation of
independence]
Many people choose P over Q and Q’ over P’
Common consequence violates
independence
P = (1 mln, 1)
P’= (1 mln, 0.11; 0, 0.89)
Q = (5 mln, 0.1; 1 mln, 0.89; 0, 0.01)
Q’= (5 mln, 0.1; 0, 0.9)
10/11 0.11 P,P'
0.11 1mln
0.89 Q,Q'
c
R
0.89 5mln
1/11 0
c
• If we plug c = 1mln, we get P and Q respectively
• If we plug c = 0, we get P’ and Q’ respectively
Common ratio violates independence
P=(3000 PLN, 1)
P’=(3000 PLN, 0.25; 0 PLN, 0.75)
Q=(4000 PLN, 0.8; 0 PLN, 0.2)
Q’=(4000 PLN, 0.2; 0 PLN, 0.8)
0.8 1 0.25 P'
P
0.75 0.25 3000
Q'
0
Q
0.75 4000
0.2 0
0
Common consequence effect in the
Machina triangle
17.1) Choose one lottery:
p2
1
1mln
P=(1 mln, 1)
Q=(5 mln, 0.1; 1 mln, 0.89; 0
mln, 0.01)
17.2) Choose one lottery:
P’=(1 mln, 0.11; 0 mln, 0.89)
Q’=(5 mln, 0.1; 0 mln, 0.9)
5mln
0
1 p1
Fanning out
p2
1
1mln
5mln
0
1 p1
Conclusion 2
15
• We often perceive probabilities as if they
didn’t conform to the laws of probability
– We prefer risk than uncertainty uncertainty
aversion (Ellsberg paradox)
– Certainty effect - we attach to high a value to
certainty (Allais paradox)
• Maximizing utility may not describe many our
choices
11 (or endowment effect)
11.1) You are given a new coffee mug (photo below). For what minimal price
would you sell it? Give a price between $1-$50.
11.2) There is a coffee mug for sale. For what maximal price would you buy it?
Give a price between $1-$50.
Kahneman, Knetsch, Thaler (1990) [endowment effect, WTA-WTP disparity]
WTA>WTP
Conclusion 3
17
• We are reluctant to depart from the status
quo
• We dont’t want to part with what’s ours or
what we bought or acquired
People usually pay more if
n=1
Expected utility implies the
opposite: 1/3 versus 1/6
Famous Zeckhauser’s
paradox
Conclusion 4
• People do not weigh probabilities evenly
– They overweigh low probabilities
– They underweigh high probabilities
Recap
28
• Behavior
– The context of decision is important (reference point, what is
gain, what is loss)
– We perceive probabilities in the wrong way (e.g. attach too
much priority to a given event)
– We are attracted too much to what we have (status quo bias)
– We like sure gains, we dislike sure losses
– We dislike losses more that we like gains (losses loom larger
than gains)
• Theory
– Expected Utility Theory does not acommodate these features
Probability weighting
Exercise