Question

Consider the matrix below that does not yet contain all the necessary payoffs. Fill in the payoffs, a and b, such that the structure of the game is equivalent to a prisoners’ dilemma.

Player 2

Player 1	F	R
F	(a,80)	(b,40)
R	(40, b)	(100,100)

Group of answer choices

None of the other answers is correct.

a=20, b=140

a=200, b=40

a=160, b=0

a=80, b=150

Answer 1

The structure of the game is equivalent to the prisoners dilemma. The prisoner dilemma is a game in which one player's strategy affects the other player. Both the player's try to maximise their pay off (i.e. make them better off). Each player chooses the strategy assuming other players strategy.
Here in the given payoff matrix we see when the player 1 and player both chooses the strategy (R,R) the pay off is (100,100). When the player 1 and player 2 chooses the strategy (F,F) the payoff should be same (a,80) so a should be 80. And thus, for the strategy (F,F) the payoff is (80,80). If both chooses same strategy the payoff for each player will be same.
The player's if doesn't chooses same strategy i.e. if one chooses F other chooses R.
The strategy is (R,F) i.e. when player 1 chooses R and player 2 chooses F. So the payoff (40,b) will be (40, 150). And similarly,
If the strategy is (F,R) i.e. when player 2 chooses R and player 1 chooses F. So the payoff (b,40) will be (150,40).

So, a=80 and b= 150