Problem 3 In the context of the previous problem suppose that a, c1 and c2 are integers and that only integer prices are allowed. Again, derive the entire set of pure strategy Nash equilibria (you can refer to he previous part if you find it convenient). What strategies survive the procedure of iterative removal of weakly dominated strategies? (A strategy s i weakly dominates s i if s i does at least as well as s i always,and strictly better sometimes.) Comment on your calculations. Remark: Withintegerpricesitispossibleformultiplepricestoyieldthesamepositivelevel of profits (even with our simple demand/cost specifications). If you find it convenient to rule out this possibility do so.

(Consider a Bertrand duopoly with homogenous products and market demand functionQ(p)= ap. Suppose marginal costs are c1 for firm 1 and c2 for firm 2 with c1 < c2 < a. Suppose that, if both firms charge the same price, all consumers buy from Firm 1. The rest of the details are just like in the slides. Derive the entire set of pure strategy Nash equilibria, justifying your conclusions as explicitly as you can.) PREVIOUS PROBLEM THAT IS NEEDED FOR THE PROBLEM NUMBER 3