In the "Rock - Scissors - Paper" game two players simultaneously throw their right arms up and down to the count of "one, two, three." On the count of three, each player forms his hand into the shape of either a rock, a pair of scissors, a piece of paper. Abbreviate these shapes as R, S and P, respectively. The players make this choice at the same time. If the players pick the same shape, then the game ends in a tie. Otherwise, one of the players wins and the other loses. The winner is determined by the following rule: rock beats scissors, scissors beats paper, and paper beats rock. Each player obtains a payoff of 1 if he or she wins, 1 if he or she loses, and 0 if he or she ties. (iv) Represent this game in the extensive form. [4] (v) Construct a payoff matrix for this game. [4] (vi) Is this game also a zero - sum game? Explain your answer. [2] (vii) Find a mixed strategy Nash equilibrium for this game. [7]