Collusion

This chapter studies firms’ incentives to collude in imperfectly competitive markets. Exercise 8.1 identifies the range of discount factors that support the collusion of two firms. Extending into a multiple firm context, Exercise 8.2 indicates that it becomes more difficult for firms to collude as the profit gain from cheating increases with the number of firms, so that every firm needs to assign a sufficiently high value on future profits to sustain collusion. We are also interested in analyzing firms’ repeated interaction when competing in prices. Exercise 8.3 investigates firms’ incentives to collude in prices when two firms sell homogeneous products. Exercise 8.4–8.5 allows for product differentiation, where we show that firms can collude under a wider range of discount rates when products become more differentiated. Exercise 8.6 examines markets with time-varying demand, showing that in markets with growing (shrinking) demand, collusion can be sustained under less (more) restrictive conditions on discount rates as the deviating firm faces larger (smaller) punishments in future periods. In sum, collusion is easier when goods are more differentiated and markets are more concentrated and expanding. Exercises 8.7 and 8.8 examine how collusive incentives are affected when firms’ production costs are convex, instead of linear. In particular, Exercise 8.7 considers that firms’ costs are symmetric, while Exercise 8.8 allows for cost asymmetries. Intuitively, all firms produce a positive output in the cartel, which becomes more attractive when firms are more asymmetric, since they can shift a larger output share to the most efficient firm, ultimately increasing cartel profits. We further consider the effects of prosecution on the stability of a cartel. Exercise 8.9 shows that collusion becomes more difficult when firms are subject to prosecution that dissolves the cartel with a positive probability in every period. Interestingly, a heavier penalty makes collusion easier to sustain since firms now have lower expected gains from output coordination that makes deviation less profitable. Exercise 8.10 illustrates that the same results hold when firms compete on prices. Exercise 8.11 investigates collusive behavior when firms exhibit economies of scope, while Exercise 8.12 examines collusive behavior under temporary punishment. We show that the tit-for-tat strategy cannot be sustained in equilibrium because one-period reversal to the Nash equilibrium output does not offset the firm’s instantaneous gain from deviation. However, the longer the punishment phrase, the more future profits that the firm loses so that collusion can be sustained under a wider range of discount rates. Exercise 8.13 studies the condition for which firms find collusion sustainable and punishment credible, where full (partial) collusion can be supported when discount factors are relatively high (low). Exercise 8.14 considers intermittent collusion, which requires higher discount factors when firms collude less frequently. Exercise 8.15 demonstrates that collusion is more difficult to sustain when prices are inflexible. Exercise 8.16, based on Exercise 7.9 , suggests that when a firm deviates from a Stackelberg cartel and loses output leadership, this firm is less likely to deviate than when it retains output leadership after the deviation, as in Exercise 8.17. Exercise 8.18 reveals that cost-reduction effects may facilitate (hinder) collusion when firms have stronger incentives to collude (defect). Exercise 8.19 evaluates leniency programs, where antitrust authorities seek to induce one of the colluding firms to provide evidence against the cartel in exchange for a pecuniary reward, such as a reduced fine or shorter prison sentences. Exercise 8.20 further shows that when the antitrust authority is able to prove firms guilty of collusion when an investigation is opened, firms still have incentives to collude when they consider investigation to be a rare event. However, once an investigation is opened, firms may pledge guilty and pay a reduced fine to provide evidence against the cartel.