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Expected Utility Theory
Expected Utility Theory
1 questions
Difficulty 6-6
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Intermediate
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counterexample
A student claims: 'Expected utility theory implies that a rational agent should always take a bet with positive expected value.' Which scenario disproves this?
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A.
Bet paying +1 dollar with prob 0.51, losing 1 dollar with prob 0.49. Positive EV (+0.02) but the agent rejects it out of irrational loss aversion
B.
Bet paying +200M with prob 0.6, losing everything with prob 0.4. Positive EV (+80M) but a log-utility agent rejects it because ruin has
−
∞
utility
C.
The St. Petersburg paradox: infinite expected value but no rational person pays infinite money, so expected value theory must be wrong entirely
D.
Lottery tickets: negative expected value but millions of people buy them, proving that rational agents sometimes reject positive EV and accept negative EV
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