Consider the following Bertrand competition model. Two firms choose their prices simultaneously and the market demand is Q(p). A firm with the lowest price serves the entire market. They split the demand equally if prices are equal. Each firm i = 1, 2 has constant unit of production (i.e., marginal cost) ci > 0 where c1 > c2,and so the firms marginal costs are different. a) Show that p1 = p2 = c1 is not a Nash equilibrium. b) Show that there is no Nash equilibrium where the firms pick the same price (i.e., p1 = p2). c) Is there a Nash equilibrium of this game? d) Suppose now that the prices are discrete and so firm is price must be a multiple of a cent: That is, pi - {0.01, 0.02, 0.03, ..., 0.01n, ...} where n is some positive integer. What is the Nash equilibrium now?
Consider the following Bertrand competition model. Two firms choose their prices simultaneously and the market demand is Q(p). A firm with the lowest price serves the entire market. They split the demand equally if prices are equal. Each firm i = 1, 2 has constant unit of production (i.e., marginal cost) ci > 0 where c1 > c2,and so the firms marginal costs are different. a) Show that p1 = p2 = c1 is not a Nash equilibrium. b) Show that there is no Nash equilibrium where the firms pick the same price (i.e., p1 = p2). c) Is there a Nash equilibrium of this game? d) Suppose now that the prices are discrete and so firm is price must be a multiple of a cent: That is, pi - {0.01, 0.02, 0.03, ..., 0.01n, ...} where n is some positive integer. What is the Nash equilibrium now?
