1.Consider a game in which there is a prize worth 30. There are three contestants, A, B, and C. Each can buy a ticket worth 15 or 30 or not buy a ticket at all. They make these choices simultaneously and independently. Then, knowing the ticket-purchase decisions, the game organizer awards the prize. If no one has bought a ticket, the prize is not awarded. Otherwise, the prize is awarded to the buyer of the highest-cost ticket if there is only one such player or is split equally between two or three if there are ties among the highest-cost ticket buyers. The final payoff to a player is the difference between the prize awarded to them the cost of the ticket they bought.

a)Write the payoff matrix for this game.

b)Find all of the game's Nash equilibria in pure strategies.

1.Consider the following two-player game:

Player 2 L C R T 0, 0 -1, 1 -2, -2 Player 1 M 1, - 1 -2, -2 1, - 1 B -2, -2 -1, 1 0. 0