Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1. Use the following game tree to answer parts a & b. At a chance node (Nature's turn) or
when a player is indifferent between strategies, each branch has equal likelihood (50%
chance they take either path). Nature receives no payoff. Assume players are mistake
proof. Use a complete strategy when discussing the results of this game and provide a
payoff, even if that payoff is an expected one. Recall that an expected payoff is the
"average" payoff: for example if with 50% chance we receive a payoff of 5 and with 50%
chance we receive a payoff of 2, the expected payoff is .5 x 5+ .5 x 2 = 3.5
a. What is the outcome of the game? Assume players are risk neutral (i.e., they see no
difference in getting a payoff of 5 vs an expected payoff of 5).
Red 0, 1, 3, 3
3, 2, 3, 2
Dorothy
Blue
Top
1, 4, 3, 2
Scarecrow
50%
Green
Nature
Right
Bottom
0, 2, 3, 1
Lion
50%
1, 3, 4, 2
3, 4, 3, 2
50%
Left
Nature
3, 2, 1, 2
Up
50%
Red.
1, 3, 4, 2
Down
Tinman
Blue
0, 3, 3, 3
Yellow
Dorothy
4, 3, 4, 2
Equilibrium:
b. Let's say Scarecrow is a gambler. By this I mean he prefers having a chance at a good or
bad outcome vs a guarantee (for example, he'd take a 50-50 shot at 10 vs. 0 vs just a
guaranteed payoff of 5, even though both have the same expected payoff). Even if
Scarecrow wasn't a gambler, would it be beneficial to him to pretend to be?
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