Game Theory Question: Please solve attached problem, and show all work, thanks

3. In a threemarket chain store game, the competitors (local stores) initially believe that the chain store is crazy with probability 0.1. The payoffs are standard (the sane chain store obtains 0 if it accommodates an entry, (1 = 2 if there is no entry and 1 if it ghts an entry; the competitor obtains b = 0.5 if it enters and is accommodated, 1 if it enters and is fought, and 0 if it stays out). Assume all players behave according to the SPE. a) What will competitor 3 (the one that begins the game) do? b) What will the chain store do in market 3 and what payoff will it obtain in that market? c) What will competitor 2 do? d) What will the chain store do in market 2 and what will be its (expected) payoff in that market? e) What's going to happen in market 1: what will competitor 1 do and what will be chain store's response. Consider different cases if necessary. f) If competitor 1 is going to randomize, what is the probability of it going out