A total of n + 1 players are bidding for a 100 payoff, with the highest bid winning the amount by which 100 exceeds the bid. Player 1 knows that the bids of players 2 through n+1 are independent uniform (0, 100) random variables.

(a) What should player 1 bid so as to maximize their expected gain.

(b) Find player 1’s maximal expected gain.

(c) Find the expected gain of player 1 if their bid is also uniform on (0, 100).