Consider a game that awards $30 worth of prize. There are three contestants: A, B, and C. Each of them decide to pay $15 or $30 for a ticket, or decide to buy no ticket at all. The three contestants make their decisions simultaneously and independently. Subsequently, after all the contestants make their respective choices, the game's organizer grants the prize based on the following rules: if no contestant bought a ticket, the price is not awarded. Otherwise, the price is awarded to the contestant who paid the highest price for the ticket if several contestants paid the highest prize, then the prize is divided equally among the contestants. The utility of a contestant is given by v - p: where v is the value of the prize that the contestant receives and p is the amount the contestant decided to pay for the ticket.
Write the game in matrix form.
Find all pure-strategy Nash equilibria.