Consider a repeated game with two players and two rounds. The stage game is shown below. Assume the players have a common discount factor & e (0, 1). Which of the following is NOT TRUE?

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Chapter1: Making Economics Decisions
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Q3

Consider a repeated game with two players and two rounds.
The stage game is shown below. Assume the players have a
common discount factor & e (0, 1). Which of the following is
NOT TRUE?
L
M
H
3, 3
2, 1
12, 0
1, 2
|6, 6
|0,0
0, 12
0, 0
|10, 10
O There doesn't exist any discount factor such that (H,H) will be
played in the first period since the game is finite.
If payoff for (L,L) is (0,0), then there is no way to sustain (H,H) in
the first period.
There is a SPNE where the two firms play (L, L) in the first period
and (M,M) in the second period.
O If the stage game is repeated for 3 times instead of 2, then the
minimum $\delta$ such that there is a SPNE where (H,H) is
played in the fırst round is smaller.
There are 2 pure strategy NE and 1 mixed strategy NE for the
stage game.
Transcribed Image Text:Consider a repeated game with two players and two rounds. The stage game is shown below. Assume the players have a common discount factor & e (0, 1). Which of the following is NOT TRUE? L M H 3, 3 2, 1 12, 0 1, 2 |6, 6 |0,0 0, 12 0, 0 |10, 10 O There doesn't exist any discount factor such that (H,H) will be played in the first period since the game is finite. If payoff for (L,L) is (0,0), then there is no way to sustain (H,H) in the first period. There is a SPNE where the two firms play (L, L) in the first period and (M,M) in the second period. O If the stage game is repeated for 3 times instead of 2, then the minimum $\delta$ such that there is a SPNE where (H,H) is played in the fırst round is smaller. There are 2 pure strategy NE and 1 mixed strategy NE for the stage game.
Expert Solution
Step 1

There are two players : Player 1 & 2 

Strategy set of both the players : { L , M , H }

Discount factor : δ [ 0, 1]δ [ 0, 1]

 
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