Prospect Theory

Kahneman, Tversky (1979) [framing, Asian disease] 1) 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:   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. 2) 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:   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 1) are exactly the same as lotteries in 2). Framing is different though. People often: Choose program A in 1 Choose program B in 2

Gains and losses Which lottery would you choose A) sure gain of $ 3 000 B) 3:1 chance of getting $ 4 000 or nothing X) sure loss of $ 3 000 Y) 3:1 chance of losing $ 4 000 or nothing

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

Many people choose P over Q and Q’ over P’ The Allais paradox 1) Choose one lottery: P=(1 mln, 1) Q=(5 mln, 0.1; 1 mln, 0.89; 0 mln, 0.01) 2) Choose one lottery: P’=(1 mln, 0.11; 0 mln, 0.89) Q’=(5 mln, 0.1; 0 mln, 0.9) Kahneman, Tversky (1979) [common consequence effect violation of independence] Many people choose P over Q and Q’ over P’ 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’

Common ratio effect 1) Choose one lottery: P=(3000 PLN, 1) Q=(4000 PLN, 0.8; 0 PLN, 0.2) 2) Choose one lottery: P’=(3000 PLN, 0.25; 0 PLN, 0.75) Q’=(4000 PLN, 0.2; 0 PLN, 0.8) Kahneman, Tversky (1979) [common ratio effect, violation of independence] Many people choose P over Q and Q’ over P’ 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’

Common consequence effect - violation of 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) If we plug c = 1mln, we get P and Q respectively If we plug c = 0, we get P’ and Q’ respectively

Common ratio effect – violation of 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)

Common consequence effect in the Machina triangle p3 5 mln 1 Q’=(5 mln, 0.1; 0 mln, 0.9) Q=(5 mln, 0.1; 1 mln, 0.89; 0 mln, 0.01) P’=(1 mln, 0.11; 0 mln, 0.89) P=(1 mln, 1) 1 mln 1 p1

Fanning out p2 1 1 p1 Q’=(5 mln, 0.1; 0 mln, 0.9) Q=(5 mln, 0.1; 1 mln, 0.89; 0 mln, 0.01) P=(1 mln, 1) 1 p1 P’=(1 mln, 0.11; 0 mln, 0.89)

Conclusion 2 Changes in probabilities are not treated linearly Certainty effect - we attach to high a value to certainty (Allais paradox)

Endowment effect 1) You are given a new coffee mug. For what minimal price would you sell it? Give a price between $1-$50. 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 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 It seems like people do not weigh probabilities evenly They overweigh low probabilities They underweigh high probabilities

Recap Behavior The context of decision is important (reference point, what is gain, what is loss) We perceive probabilities in the subjective 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