1. Differentiated Bertrand Competition. There are two firms i = 1, 2 simultaneously choosing prices pi [0, 1]. The demand of firm i is Di(pi , pi) = 1 3pi + pi and it has zero production costs. That is, firm is payoff is piDi(pi , pi).

(a) Find the best response function of firm i.

(b) Find the set of 1-rationalizable, 2-rationalizable and 3-rationalizable strategies.

(c) Find the unique PSNE.

please no handwring and this course about game theory (topic Rationalizability)

answer with all steps please