Suppose 2 players are competing in a raffle for a single prize. The price of each raffle ticket is 1. The value of the prize to both players is V. Each player's chance of winning is equal to the number of raffle tickets the player purchases divided by the total number of tickets purchased by both players. That is, if player 1 buys T tickets, and player 2 buys T tickets, player 1's chance of winning is T/(T+T), and player 2's chance of winning is T/(T+T). The players are risk neutral, so that if player i wins the prize, player i's utility is V-T where Ti is the number of tickets player i bought. Alternatively, if player i loses, player i's utility is O-Ti. a. Write down player 1's expected payoff as a function of V, T, and T. b. Derive player 1's best response function, as a function of V and Tz. c. Write down player 2's expected payoff function and best response function. d. Find the Nash equilibrium number of tickets purchased by each player.