PROBLEM SET 3 Econ 250 . Deerentiated Bertrand Competition. There are two rms 2' = 1, 2 simultaneously choosing prices p1; E [0,1]. The demand of rm 1' is D,(p,,p_,-) = 1 3p, + p_, and it has zero production costs. That is, firm i's payoff is p,D,[p,, p_,). (a) Find the best response function of rm i. (b) Find the set of 1rationalizable, 2rationalizable and 3rationalizable strategies. (0) Find the unique PSNE. . Consider the following Guessing Game. There are n = 10 players simultaneously choosing a number in {1,2, 3}. The winners are those closest to 1/2 the average guess {they evenly split the prize between the winners if there is more than one). Find the set of rationalizable strategy proles. Justify your