PBE stands for perfect Bayesian equilibrium

Part 2 2. In a chain store game with four cities, the payoffs are as was discussed in class with a - 1.5 and b - 0.5. Initially, the local stores believe that the chain store is crazy with probability Pc - 0.1. a) Which local store will be the first to enter in the PBE of this game? b) What will the chain store do in that city? c) What will the next local store do in the PBE? Consider all possibilities in case there are more than one. d) If the local store 1 can use a mixed strategy under certain circumstances of the PBE, what is the probability of it entering the game (i.e. choosing the In action)? Hint: This probability can be found from the condition of the chain store being indifferent between its two actions when it randomizes in the previous period. e) What is the expected payoff of the chain store in the PBE