1 / 25

How Could The Expected Utility Model Be So Wrong?

How Could The Expected Utility Model Be So Wrong? . Tom Means SJSU Department of Economics Math Colloquium SJSU December 7, 2011. The Expected Utility Model. 1 – Decision Making under conditions of uncertainty Choose option with highest expected value.

teryl
Télécharger la présentation

How Could The Expected Utility Model Be So Wrong?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. How Could The Expected Utility Model Be So Wrong? Tom Means SJSU Department of Economics Math Colloquium SJSU December 7, 2011

  2. The Expected Utility Model. • 1 – Decision Making under conditions of uncertainty • Choose option with highest expected value. • 2 – Utility versus Wealth. (St. Petersburg paradox) • Flip a fair coin until it lands heads up. You win • 2n dollars. E(M) = (1/2)($2) + (1/4)($4) + …. = ∞ • 3 – Ordinal versus Cardinal Utility

  3. The Expected Utility Model. • 4 – Maximize Expected (Cardinal) Utility. • E[U(M)] = Σ Pi × U(Mi) • (The Theory of Games and Economic Behavior, John von Neumann and Oskar Morgenstern

  4. Attitudes Toward Risk. • 1 – Comparing E[U(M)] with U[E(M)] • Risk-Aversion; E[U(M)] <U[E(M)] • Risk-Neutrality; E[U(M)] =U[E(M)] • Risk-Seeking; E[U(M)] > U[E(M)]

  5. Risk Aversion; X = { 1-P, $20; P, $0} Utility of dollars U($) U(20) e $4 20 Dollars 0 e’ 18 16 Tom is indifferent between not buying insurance and having an expected utility equal to height e’e, and buying insurance for a premium of $4 and having a certain utility equal to the value of the utility function at an income of $16.

  6. Risk-preferring Utility of dollars U($) b U(38) .10(18)+.90(38) d U(18) 38 Dollars 0 b’ d’ 36 18 Kathy will not sell insurance to Tom at a zero price because she prefers a certain utility equal to height b’b rather than an expected utility equal to height d’d.

  7. Willingness to sell insurance Utility of dollars U($) U(38) k b U(18) 38+1.5=39.5 Dollars 0 k’ b’ 38 18+1.5=19.5 38+π 18+π Kathy is indifferent between not selling insurance and having a certain utility equal to height b’b, and selling insurance at a premium of $1.50 and having an expected utility equal to height k’k.

  8. Measuring Risk Aversion • U[E(M) – π) = E[U(M)] • Arrow/Pratt Measure π ≈ -(σ2/2)U’’(M)/U’(M) • Absolute Risk Aversion r(M) = U’’(M)/U’(M) • Relative Risk Aversion r(M) = M × r(M)

  9. Some Observations • Individuals buy insurance (car, life, fixed rate mortgages, etc) and exhibit risk aversion • Risk-averse individuals go to casinos. • Freidman/Savage article • Ellsberg, Allais, Kahneman/Taversky

  10. How Could Expected Utility Be wrong?E[U(M)] = Σ Pi × U(Mi) • Violations of probability rules • Conjunction law • The Linda problem. P(A & B) > P(A), P(B) • (Daniel Kahnemanand Amos Tversky) • Ambiguity aversion • The Ellsberg Paradox (known vs. ambiguous distribution) • Base rates • Nonlinear probability weights • Framing

  11. Framing Problem One. Pick A or B A:X = { P = 1, $30; 1-P = 0, $0} B: X = {0.80, $45; 0.20, $0}

  12. Framing Problem Two. Stage One. X = { 0.75, $0 and game ends; 0.25, $0 and move to second stage} Stage Two. Pick C or D. C: X = { P = 1, $30; 1-P = 0, $0} D: X = {0.80, $45; 0.20, $0}

  13. Framing Problem Three. Pick E or F E: X = {0.25, $30; 0.75, $0} F: X = {0.20, $45; 0.80, $0} X + C = E X + D = F

  14. How Could Expected Utility Be wrong? • Violations of probability rules • Constructing values – Absolute or Relative, Gains versus Losses Choosing an option to save 200 people out of 600. Choosing an option where 400 out of 600 people will die.

  15. The Kahneman-Tversky Value Function

  16. The Benefit of Segregating Gains

  17. The Benefit of Combining Losses

  18. The Silver-Lining Effect and Cash Rebates

  19. How Could Expected Utility Be wrong? • Violations of probability rules • The reflection effect. Do people value gains different than losses? Prospect Theory. Chose between A or B • A: X = { 1.0, $240; 0.0, $0} • B: X = {0.25, $1000; 0.75, $0} Chose between Cor D • C: X = { 1.0, $-750; 0.0, $0} • D: X = {0.75, $-1000; 0.25, $0}

  20. How Could Expected Utility Be wrong? • Violations of probability rules • The reflection effect. Do people value gains different than losses? Prospect Theory. Chose between E or F • E: X = { 0.25, $240; 0.75, -$760} • F: X = { 0.25, $250; 0.75, -$750}

  21. How Could Expected Utility Be wrong? • Violations of probability rules • The reflection effect. Do people value gains different than losses? Prospect Theory. A preferred to B (84%) D preferred to C (87%) F preferred to E (100%)

  22. How Could Expected Utility Be wrong? • Violations of probability rules • The reflection effect. Do people value gains different than losses? Prospect Theory. A(84%) + D (87%) = E B + C = F

  23. How Could Expected Utility Be wrong? • Violations of probability rules • Scaling of Probabilities. Chose between A or B • A: X = { 1.0, $6000; 0.0, $0} • B: X = {0.80, $8000; 0.20, $0} Chose between Cor D • C: X = { 0.25, $6000; 0.75, $0} • D: X = { 0.20, $8000; 0.80, $0}

  24. How Could Expected Utility Be wrong? • Violations of probability rules • Scaling Probabilities. A preferred to B and D preferred to C E[U(A)] > E[U(B)] implies E[U(C)] > E[U(D)] E[U(A)]/4 > E[U(B)]/4 and add 0.75U(0) to both sides to show E[U(C)] > E[U(D)]

  25. How Could The Expected Utility Model Be So Wrong? • Questions/Comments

More Related