a Suppose you are given a choice between thefollowing options:A1: Win $30 for sureA2: 80% chance of winning $45 and 20% chance ofA2: winning nothing B1: 25% chance of winning $30B2: 20% chance of winning $45Most people prefer A1 to A2 and B2 to B1. Explainwhy this behavior violates the assumption that decisionmakers maximize expected utility.b Now suppose you play the following game: You havea 75% chance of winning nothing and a 25% chance ofplaying the second stage of the game. If you reach thesecond stage, you have a choice of two options (C1 andC2), but your choice must be made now, before youreach the second stage.C1: Win $30 for sureC2: 80% chance of winning $45 13.5 Bayes’ Rule and Decision Trees 767Most people choose C1 over C2 and B2 to B1 (from part(a)). Explain why this again violates the assumption ofexpected utility maximization. Tversky and Kahneman(1981) speculate that most people are attracted to thesure $30 in the second stage, even though the secondstage may never be reached! Note that B1 and C1 bothgive $30 with the same probability, and B2 and C2 bothyield $45 with the same probability. It appears thatpeople do not act very rationally!†
a Suppose you are given a choice between the
following options:
A1: Win $30 for sure
A2: 80% chance of winning $45 and 20% chance of
A2: winning nothing
B1: 25% chance of winning $30
B2: 20% chance of winning $45
Most people prefer A1 to A2 and B2 to B1. Explain
why this behavior violates the assumption that decision
makers maximize expected utility.
b Now suppose you play the following game: You have
a 75% chance of winning nothing and a 25% chance of
playing the second stage of the game. If you reach the
second stage, you have a choice of two options (C1 and
C2), but your choice must be made now, before you
reach the second stage.
C1: Win $30 for sure
C2: 80% chance of winning $45
13.5 Bayes’ Rule and Decision Trees 767
Most people choose C1 over C2 and B2 to B1 (from part
(a)). Explain why this again violates the assumption of
expected utility maximization. Tversky and Kahneman
(1981) speculate that most people are attracted to the
sure $30 in the second stage, even though the second
stage may never be reached! Note that B1 and C1 both
give $30 with the same probability, and B2 and C2 both
yield $45 with the same probability. It appears that
people do not act very rationally!†
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