Question

Game Theory:

John and Dave are playing a game where they only have two strategies, either to move left or move right. The payoffs from this game are the points that each player will earn given the strategies that each play. The higher the points, the higher the payoffs each player will receive. The normal form representation of the game is presented below.

                                                   DAVE

                        Left                                                  Right

Left 1,1	0,3
Right 3,0	2,2

John's name label should be on the left side.

a. Does either player in the above game have a dominant strategy? If yes, what is it?

b. Does the game shown above have a dominant strategy equilibrium? If yes, what is it?

c. Does the game shown above have a Nash Equilibrium? If yes, what is it?

d. Is this game an example of the Prisoner's Dilemma? Why or why not?

e. If a game is repeated indefinitely, explain how the Tit for Tat strategy can get players out of the Prisoner's Dilemma.

Answer 1

A) given dave move left, best response for john is right

given dave move right, best response for john is right

So john has dominant strategy of righ

By same reasoing ,dave also ahs a dominant strategy of right.

B) Dominant strategy equilibrium,when both players choose theirs dominant strategy .

So dominant strategy nash equilibrium:(john,dave):(2,2)

C)Yes , dominant strategy equilibrium is the nash equilibrium

D)No, because dominant strategy equilibrium gives is the collusion equilibrium.

E) Because game is not in form of prisnor dilemma ,so there is no need of tit for tat strategy .