Question

Exercise 6 (Difficult),. Consider the following modification of the prisoner's dilemma game. A-1,-1-9,0-6,-2 B | 0,-9 |-6-61-5-10 C1-2,-6 |-10,-51-4,-4 You should recognise the payoff's from (A, L), (A, R). (B, L). (B, R) as those in the prisoner's dilemma game studied in class. We added two strategies, one for each player. Also note that strategies A and L are still (when compared to the original prisoner's dilemma game) strictly dominated . What is the set of Nash equilibria of this game. Suppose that the two players play this game twice. After they play the first time, payments are made and each player knows the action chosen by the other player. Then they play a second time. Is there a subgame perfect equilibrium where players play (A,L) the first time the play the game? (For simplicity you may focus on subgame perfect equilibria where players do not use randomised choices.)

Answer 1

The set of nash equilibria of this game { (-1,-9),(-9,-6),(-5,-4),(-2,-9)}

equilibria attain when domain of a sertain sample = range of the another sample. by doing that we get the solution of the nash equilibria.