PROBLEM (3) (Regret Aversion, Gale's Roulette Wheels) Consider the regret utility u(x, y) = {1 if x>y, 0 if x=y, and -1 if x

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PROBLEM (3) (Regret Aversion, Gale's Roulette Wheels) Consider the regret utility
u(x, y) = {1 if x>y, 0 if x=y, and -1 if x<y } and the independent gambles A, B and C where
A delivers $2, or $4, or $9 with 1/3 probability each.
B delivers $1, or $6, or $8 with 1/3 probability each.
C delivers $3, or $5, or $7 with 1/3 probability each.
a) Calculate the expected regret utilities U(A|B), U(B|C), U(C|A). How does the agent rank A, B, C lotteries; is
there a preference cycle (intransitivity)?
b) Is there a lottery that delivers $x for sure (with probability 1) and is better than B but worse than A?
Transcribed Image Text:PROBLEM (3) (Regret Aversion, Gale's Roulette Wheels) Consider the regret utility u(x, y) = {1 if x>y, 0 if x=y, and -1 if x<y } and the independent gambles A, B and C where A delivers $2, or $4, or $9 with 1/3 probability each. B delivers $1, or $6, or $8 with 1/3 probability each. C delivers $3, or $5, or $7 with 1/3 probability each. a) Calculate the expected regret utilities U(A|B), U(B|C), U(C|A). How does the agent rank A, B, C lotteries; is there a preference cycle (intransitivity)? b) Is there a lottery that delivers $x for sure (with probability 1) and is better than B but worse than A?
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