Consider the stage game above and suppose it is repeated twi

Consider the stage game above and suppose it is repeated twice without discounting. There exist a SPNE in which the first period outcome is (B,D). To support this SPNE player 1 plays action B in the first period and action__ in the second period. Player 2 plays action D in the first period, and plays action__ in the second if the first period outcome was (B,D) and plays action otherwise__

choose 1 letter for each of the 3 spots

Solution

Solution: Since the game is two stage game without discounting factor, then players can get highest payoff if they aggree to play (B,D) in first period and (A,D) in second period.

Since player 1 has strategy A as his dominant strategy no matter what player 2 plays. Given this public information player 2 can play strategy C and D as he gets equal payoff 1 on both.

If there exist a SPNE in which first period outcome is (B, D) then player 1 would play his dominant strategy A as game is going to end after second period. To sustain the SPNE player 2 must ensure that he would play D in second period if (B, D) was the first period strategy and plays acton otherwise C, because it gives a potential threat to player 1 to play B in first period otherwise he can play A in period one since he gets (7+7) = 14 > (4+7)= 11. Player 2, by playing C (if (B, D) was not a outcome in first period) would end the as (1+7)=8 < 11 for player 1.

So in SPNE the final payoff would be (11, 6).

So A , D, C are the final answers.