Question

Determine the Nash-Bargaining solution of a prisoner dilemma.

     C        D

C (2,2) (0,3)

D (3,0) (1,1)

Answer 1

Player one is the horizontal player and player two is the vertical player.

Consider player one,

If player one knows/thinks that player two will choose to play C, the better option for him is to choose D because his payoff is more with D than C in this case( 3>2). So he would choose D.

If player one thinks that player two will choose to play D, then he will again choose D as he gets more payoff with D(1>0).

So, player one will choose to play D whatever the choice be for player two. It is player one's dominant strategy to play D.

Similarly we can consider player two,

If one chooses C, player two will play D as (3>2)

If one chooses D, player two will play D as well as (1>0)

Thus, playing D is dominant strategy for both players.

The Nash equilibrium for this game will be (D, D) =(1, 1).

Had the players cooperated they could have got payoff of 2 each but they only get payoff of 1 each due to non corporation. This game is called prisoners dilemma as two rational individuals reach a decision that is not Pareto optimal.