In general, cooperation in a finitely repeated game is not a SPE with a 2x2 prisoners dilemma.
Question:
In general, cooperation in a finitely repeated game is not a SPE with a 2x2 prisoner’s dilemma. But, there are other cases where cooperation may hold as the outcome of a SPE. Consider the following 3x3 prisoner’s dilemma stage game, to be repeated twice with no discounting.
A
Define the following strategy Si for player i.
• Play R in round 1.
• In round 2, play if ; otherwise play .
(a) Are any SPE where (R,R) is played in the second round?
(b) Fill in the blanks of Si such that (SA,SB) is a SPE of the repeated game (recall: twice repeated with no discounting)?
(c) Are there other SPE where (R,R) is played in the first round?
(d) Are there other NE of the game where (R,R) is played in the first round?
(e) Are there other SPE where (R,R) is NOT played in the first round?
Expert Answer:
The detailed answer for the above question is provided below a Yes there are SPE where RR is played ... View the full answer
