Critiques of Expected Utility Theory 14.123 Microeconomic Theory III Muhamet Yildiz Allais Paradox Choose A or B, then C or D. (A) Win $1 million for sure. (B) Win $5M with 10% chance, $1M with 89%, nothing with 1%. (C) Win $1M with 11% chance, nothing with 89%. (D) Win $5M with 10% chance, nothing with 90%. Choice of A and D violates expected utility: 1Allais Paradox, Graphically Pr($0) Pr($5) 1 1 0 A ∙ ∙∙ B C D ∙ “Common consequence” paradox: A B but D C. B’ ∙ Indifference curves “Common ratio” paradox: A B’ but D C. Resolutions indifference curves fan out. Betweenness without Independence Weighted Expected Utility: W(p) = ∑x∈X γ(x)p(x)u(x)/[∑x∈X γ(x)p(x)]. Rank-Dependent Expected Utility R(p) = ∫ u(x) dw(p(x)). And many others 2Probability Weighting Function p w 0 1 1 Ellsberg Paradox An urn contains 99 balls, colored, Red, Black and Green There are 33 Red balls; the combination of the other colors is not known. You choose a color and we draw a ball. If the ball is of the color chosen, you win $1. What color would you choose? If the ball is not of the color chosen, you win $1. What color would you choose? 3Resolution: Ambiguity Aversion Compounded lotteries are not reduced to simple lotteries Ambiguity aversion: maxa minp Ep[u(a)] Smooth ambiguity aversion: maxaE[v(Ep[u(a)])] Framing “Outbreak of disease is about to kill 600 people. Choose treatment program A or B; then C or D.” (A) 400 people die. (B) Nobody dies with 1/3 chance, 600 people die with 2/3 chance. (C) 200 people saved. (D) All saved with 1/3 chance, nobody saved with 2/3 chance. 78% of subjects pick B, 28% of subjects (in different group) pick D. But A is equivalent to C, B is equivalent to D (apart from wording). 4Prospect Theory “Edit the decision problem” Distort the probabilities using inverted S shape Apply a reference-dependent S shaped utility function Risk aversion towards gains Risk taking towards losses “Loss aversion” Prospect Theory Reference-dependent Utility Function u xx0 5Prospect Theory Formula U(x|w,x₀) = ∫u(x|x₀)dw(F(x)) Properties & Problems: What is reference point? Framing Dynamic Programming 6MIT OpenCourseWarehttp://ocw.mit.edu 14.123 Microeconomic Theory III Spring 2010 For information about citing these materials or our Terms of Use, visit:
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