Moving to another question will save this response Question

Moving to another question will save this response. Question 11 Consider the stage game below, and suppose it is repeated infinitely many times. Player 2 D E F A 1,1 1,1 1,1 Player I B 1,8 7,5 1,1 c 5,7 8,3 1,1 To sustain a SPNE in which piayers play B.3 in every period by means of a trigger strategy, the discount rate must be larger than or equal to h.(BE) cannot be pat of a SPNE E 13 A Movng to arother question will save this response.

Solution

Here punsihment is given forever once any of the player deviates. Hence there are two outcome possible for this subgame: (B, E) in for all periods including the current one or (C, F) in all periods as the punishment is given forever.

For the first case, player 1’s payoff is 7 for infinite period. If he deviates in first period he will be able to secure 8 in that period but will receive only 1 for each period forever. Hence the payoff is 8 + + ² + ... = 8(1) + . The player has no incentive to deviate if the payoff from not deviating exceed the payoff from deviating:

7 8(1) +

7 8 8 +

7 8 – 7

1/7

For the second case, player 2\'s payoff is 5 for infinite period. If he deviates in first period he will be able to secure 8 in that period but will receive only 1 for each period forever. Hence the payoff is 8 + + ² + ... = 8(1) + . The player has no incentive to deviate if the payoff from not deviating exceed the payoff from deviating:

5 8(1) +

5 8 8 +

5 8 – 7

3/7

Hence the correct option is 3/7. Option A is correct.