consider two firms that produce identical products and compete in pric
Consider two firms that produce identical products and compete in prices (i.e. their strategies are their prices). The demand function is given by q = 1 - p where q is the quantity demanded and p is the lower price of the two. The marginal cost of firm 1 is 0,and the marginal cost of firm 2 is c2 < 1. The prices charged by firm 1 and firm 2 are denoted by p1 and p2, respectively. If pl = p2, then the demand is shared equally between the two firms. a) Suppose c2 = 0. Show that pl = p2 = 0 is a Nash equilibrium, by demonstrating that neither firm deviates from the equilibrium strategy. b) Suppose 0 < c2 < 1. Show that there is no Nash equilibrium such that p1 = p2.Hint: you need to look at three different cases, namely pl = p2 < c2, p1 = p2 = c2, and p1 = p2 > c2.
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