Consider the extensive form game portrayed below. The top number at a terminal node is player 1’s payoff, the middle number is player 2’s payoff, and the bottom number is player 3’s payoff. a. Derive the strategy set for each player. (Note: If you do not want to list all of the strategies, you can provide a general description of a player’s strategy, give an example, and state how many strategies are in the strategy set.) b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it is not a SPNE.
Consider the extensive form game portrayed below. The top number at a terminal node is player 1’s payoff, the middle number is player 2’s payoff, and the bottom number is player 3’s payoff. a. Derive the strategy set for each player. (Note: If you do not want to list all of the strategies, you can provide a general description of a player’s strategy, give an example, and state how many strategies are in the strategy set.) b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it is not a SPNE.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Consider the extensive form game portrayed below. The top number at a
terminal node is player 1’s payoff, the middle number is player 2’s payoff,
and the bottom number is player 3’s payoff.
a. Derive the strategy set for each player. (Note: If you do not want to list
all of the strategies, you can provide a general description of a player’s
strategy, give an example, and state how many strategies are in the
strategy set.)
b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it is
not a SPNE.
Transcribed Image Text:1
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2
b2
b2
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b2
d2
1
1
3
d,
e, d,
bz d3
b3
1
az
2
1 3
O 3
2
1
1
2
1
2
1
1 3
2 2
2.
N O N
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