Suppose 100 players are playing a 1.25-Beauty Game, where participants select a number between 1 and 99. The goal is to be as close as possible to 1.25 the average.

(a) What are possible bids for somebody who is a D-0 level thinker? A D-1 level?

(b) What will somebody who is a L-1 thinker bid? What about L-2? Assume that L-0 thinkers bid randomly.

(c) Now consider a C-2 player who thinks that 5% of the population will play "spoiler" and bid 1, 15% are L-0 of a different type that bids randomly, and the rest are L-1 players. What will this person bid?