Optimal Timing of Cartel Formation Under Uncertainty

Understanding how business cartels form and expand is foundational for developing sound deterrence strategies. Past work (i.e. Connor, 2005) has relied on net present value (NPV) methods to evaluate the streams of costs and benefits of forming or joining a cartel. While NPV adequately measure the expected value of future streams of benefits and costs, higher moments of the distribution are also important in understanding agent behavior. Thus, in the presence of uncertainty about future streams and litigation costs, NPV may miss important dimensions that shape the issue. The decision to form or join a cartel is, at least, partially irreversible, because it exposes the firm or its involved managers to litigation on all previous returns and even after the cartel is dissolved. In this study, we rely on the aforementioned irreversible and uncertain nature of cartel participation and returns to develop a real-options framework that examines the optimal decision rules regarding the timing of cartel formation. This leads to suggestions for improved policy tools for antitrust agencies. In our model, all firms outside of a cartel essentially hold the option to form or join a cartel at some point in the future. The option is exercised the day the cartel is formed and has no cash value before that. The payoffs that firms give up by not immediately forming a cartel are weighed against uncertain and partially irreversible forming decision nature. Under the assumption of stochastic market demand, we find a threshold level of demand beyond which the cartel is formed. This threshold is analytically calculated as a function of a number of parameters. We then illustrate the conditions that determine the optimal timing decision of cartel formation by conducting comparative dynamics analysis. The timing of cartel formation is analyzed in both domestic and international settings. The qualitative results are obtained by comparative dynamics analysis and the quantitative results by numerical analysis. The results obtained in this study will assist in the development and improvement of guidelines to deter the formation of cartels by antitrust agencies in both developed and developing nations. In the first scenario of domestic cartel formation, at the beginning of each period, firms will choose to compete when the sunk costs related to a cartel operation are too high, current period demand is too low, and/or the expected duration of collusion is too short. Obviously, the possibilities of cartel formation increase when sunk costs go down, demand increases, or relationships with firms improve the prospects for a longer cartel arrangement. The value of waiting increases with a) increased uncertainty of market demand, b) increase irreversibility, and c) increased number of firms and d) a higher discount rate. We study the effect of demand uncertainty on the expected social welfare of cartel formation. The simulation results suggest that the expected social welfare under uncertainty could be higher than that under certainty. In a second scenario, we study the formation of international cartels. The model considers two markets with demand uncertainty that is either correlated or uncorrelated. The demand shocks in each market are assumed to follow geometric Brownian motion. We calculate the threshold value of demand faced by the cartel and obtain the rules guiding a firm's decision to form an international cartel. The comparative dynamics results obtained in the previous domestic scenario still apply. The simulation results suggest that cartel formation is most likely to occur between firms that come from countries with highly correlated markets and similar expected demand growth.