Two Friends,Pat and Julie,are Going to a Concert

Essay

Two friends,Pat and Julie,are going to a concert.They play a simple game in which they hold out one or two fingers to decide who will pay for the other's ticket.Pat wins if the fingers held out add up to an even number; Julie wins if the fingers held out add up to an odd number.The price of the ticket is $9.
a)Construct a payoff matrix for the game.
b)Is there a unique Nash equilibrium in this game?
c)Which strategy should a player use to maximize her chances of winning the game?