Homework Answers
Solution: The game is following that player 1 choose in period 1 followed by player 2's choice and then player 1 choose. To get the SPNE of this game we will use the Backward Induction methods.
Claim: There are two SPNEs in this game as SSS and CCC.
Player 1 at history (CC0) is indifferent by chossing S and C as he gets the same payoff as 3.
Case1:
Suppose he chose S then knowing this strategy player 2 will chose S at history (C0) as he gets higher payoff 2 > 1.
Giving this strategy player 1 will chose S at history(0) as he gets higher payoff by chosing S ( 1 >0) .
Hence SSS is one of the SPNE.
Case 2:
Suppose he chose C then knowing this strategy player 2 will chose C at history (C0) as he gets higher payoff 3 >2.
Giving this strategy player 1 will chose C at history(0) as he gets higher payoff by chosing C ( 3 >1) .
Hence CCC is an another SPNE of this game.
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