9.17 COLLUSION AND PRICE Wsimultaneously set prices (as in the Bertrand model); and if some firm sets a lower pricethan other firms, then all firms must match that price. Show that any price between costand monopoly price can be obtained as the play of a Nash equilibrium.CHALLENGING EXERCISES9.17. NUMBER OF COMPETITORS. Consider an n firm homogeneous-good oligopoly withconstant marginal cost, the same for all firms. Let 6 be the minimum value of the dis-count factor such that it is possible to sustain monopoly prices in a collusive agreement.Show that is decreasing in n. Interpret the result.9.18. Two MARKETS. Consider the model of multimarket contact presented inSection 9.3. Determine the minimum value of the discount factor such that theoptimal collusive solution is stable.9.19. SECRET PRICE CUTS. This exercise formalizes the model of secret price cups pre-sented in Section 9.2.35 Suppose that all consumers are willing to pay u for the (homoge-neous) product sold by two duopolists. In each period, demand can be high (probability1-a) or low (probability a). When demand is high, h = 1 units can be sold at price u

A market structure body by a solo seller, selling a unique product in the market. In a monopoly…

simultaneously set prices (as in the Bertrand model); and if some firm sets than other firms, then all firms must match that price. Show that any price and monopoly price can be obtained as the play of a Nash equilibrium. CHALLENGING EXERCISES 9.17. NUMBER OF COMPETITORS. Consider an n firm homogeneous-good ol constant marginal cost, the same for all firms. Let 8 be the minimum val count factor such that it is possible to sustain monopoly prices in a collusi Show that is decreasing in n. Interpret the result. 9.18. Two MARKETS. Consider the model of multimarket contact Section 9.3. Determine the minimum value of the discount factor s optimal collusive solution is stable. 9.19. SECRET PRICE CUTS. This exercise formalizes the model of secret pr sented in Section 9.2.35 Suppose that all consumers are willing to pay u for neous) product sold by two duopolists. In each period, demand can be hig 1-a) or low (probability a). When demand is high, h = 1 units can be s