This question formalizes what we discussed in lecture about the justification for the assumption that players do not play weakly dominated strategies. When we solved the Bertrand duopoly example in lecture we came down to the 2x2 game below. We then eliminated the price of 3 because that strategy is weakly dominated by charging a price of 2. The solution by iterated deletion was the profile (2,2). But deleting 3 also means eliminating the Pareto superior profile (3,3). Moreover, no firm has any positive incentive to deviate from (3,3,), which is to say that it is Nash. To formalize the underlying argument for eliminating 3, suppose that F1 believes that F2 intends to follow a strategy of charging 3 but that there is always some small residual chance that F2 will actually charge 2. In other words, F1 believes that F2 is playing a mixed strategy of charging 3 with probability 1 - c and 2 with probability c, where c can be arbitrarily small but is always positive (c > 0). F2 $2 (c) $3 F1 $2 50, 50 100,0 $3 0, 100 100, 100 (a) Show that Fl's best reply to this strategy to play 2 for sure when c > 0. (b) What is/are Fl's best replies when c = 0