Alex and Mary are trying to win a prize in a school rae (lottery). They can buy either 0, 1, 2, or 3 tickets. They are the only people in the rae, and each ticket has an equal chance of winning. Example: if Alex buys 2 tickets and Mary buys 3 tickets, then Alex has a 2/5 chance of winning and Mary has a 3/5 chance of winning. The prize is worth $60, and both care about their expected payos. Example: if Alex has a 2/5 chance of winning, her expected payo is $24. Model the following situation with strategic form games.

The people running the rae choose how much tickets cost. They want to make as much money as possible. Assume that given the cost of rae tickets, Alex and Mary play the Nash equilibrium most favorable to those running the rae (ie if there is more than one Nash equilibrium, assume they play the one in which the most tickets are sold). Which price should the people running the rae choose? Is it possible for them to sell more than $60 worth of tickets?