Brothers: Consider the following game that proceeds in two stages: In the first stage one brother (player 2) has two $10 bills and can choose one of two options: he can give his younger brother (player 1) $20 or give him one of the $10 bills (giving nothing is inconceivable given the way they were raised). This money will then be used to buy snacks at the show they will see, and each $1 of snacks purchased yields one unit of payoff for a player who uses it. In the second stage the show they will see is determined by the following Battle of the Sexes game:
a. Present the entire game in extensive form (a game tree).
b. Write the (pure-) strategy sets for both players.
c. Present the entire game in one matrix.
d. Find the Nash equilibria of the entire game (pure and mixed strategies).