Problem 4 Consider a two-stage game where two players, Ann and Beth, must first decide on a game to play (either prisoner's dilemma or stag hunt), and, if they agree, play that game. If they do not agree to play the same game, neither player receives any payoff. The game is summarized below: Beth cooperate 2,2 defect 0,3 Ann cooperate Beth prisoner's dilemma stag hunt defect Beth cooperate 3,0 Ann prisoner's dilemma stag hunt 0,0 defect 1,1 Beth prisoner's dilemma 0,0 Beth stag 3,3 stag hare hare Ann stag hunt 0,2 Beth stag 2,0 hare 1,1 a) Find the minimal proper subgames. b) Find the SPNE.

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Chapter1: Making Economics Decisions
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Problem 4
Consider a two-stage game where two players,
Ann and Beth, must first decide on a game to play
(either prisoner's dilemma or stag hunt), and, if they
agree, play that game. If they do not agree to play
the same game, neither player receives any payoff.
The game is summarized below:
2.2
Beth cooperate
defect
Ann cooperate
0,3
Beth prisoner's
dilemma
defect
Beth cooperate
3,0
Ann prisoner's
dilemma
stag hunt
stag hunt
0,0
defect
1,1
Beth prisoner's
dilemma
stag hunt
0,0
Beth
stag
3,3
stag
hare
0,2
Ann
hare
Beth stag
2,0
hare
1,1
a) Find the minimal proper subgames.
b) Find the SPNE.
Transcribed Image Text:Problem 4 Consider a two-stage game where two players, Ann and Beth, must first decide on a game to play (either prisoner's dilemma or stag hunt), and, if they agree, play that game. If they do not agree to play the same game, neither player receives any payoff. The game is summarized below: 2.2 Beth cooperate defect Ann cooperate 0,3 Beth prisoner's dilemma defect Beth cooperate 3,0 Ann prisoner's dilemma stag hunt stag hunt 0,0 defect 1,1 Beth prisoner's dilemma stag hunt 0,0 Beth stag 3,3 stag hare 0,2 Ann hare Beth stag 2,0 hare 1,1 a) Find the minimal proper subgames. b) Find the SPNE.
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