A Simple Model of Imperfect Competition in which Four are Few but Three are Not
构建了一个非完全竞争模型，发现合谋可能性并非随企业数量单调递减，这与传统寡头模型不同，关键假设是合谋被发现后会受到罚款和赔偿惩罚。
This paper presents a model of imperfect competition in which the likelihood of collusion is not a monotonically decreasing function of the number of firms. Other notable oligopoly models predict a monotonic relationship. The difference in predictions is a consequence of our assumptions that firms either explicitly collude or instead engage in Cournot behavior and that explicit collusion, if detected, is punished with fines and damages. THERE ARE few notable models of the formation or maintenance of collusive agreements. Two particularly interesting ones are those of Stigler [1964] and Selten [1973]. Stigler considers only a certain aspect of cartel maintenancedetecting cheating-while Selten considers only certain aspects of cartel formation. Their models produce the intuitive result that the likelihood of successful collusion is a monotonically decreasing function of the number of firms. We present a simple model of cartel formation and maintenance that produces a different result; it is quite possible for the likelihood of collusion to increase as the number of firms increases. An important, realistic feature of the model (at least for the United States), which distinguishes it from those of Stigler and Selten and which is partially responsible for its counterintuitive result,-is that collusion, if discovered, is punished through fines, imprisonment, and treble damage awards. Consider a simple, static model with n identical firms that either colLude explicitly and set the monopoly quantity or instead engage in Cournot behavior.' If the firms collude, they (as a group) incur costs of forming and maintaining their agreement, M, which are an increasing function of n. In addition, there is some probability, 0, that the cartel will be detected,2 in which case each firm in the cartel must pay a fixed fine, F, and the cartel must * The views expressed here are not necessarily those of the US Department of Justice. 1 To make the model very simple, we assume all-or-nothing cartels, that is, all firms are in any cartel. The specific assumption of Cournot behavior is not critical. The same basic results are obtained provided that the alternative to explicit collusion is not competition and provided that, absent explicit collusion, the fewer the number of firms, the greater is the difference between the equilibrium price or quantity and the competitive price or quantity. 2For simplicity, we assume that 0 is a constant. It may be more plausible that 0 is an increasing function of n. The more firms there are in a cartel, the more likely it may be that one will inform on the cartel. Increasing the number of firms in a cartel also increases the effort necessary to maintain cartel discipline and, therefore, may increase the likelihood that those efforts will attract the attention of enforcement authorities. If 0 were assumed to increase significantly as n is increased, the probability of collusion would be a monotonically decreasing function of n for most, perhaps all, parameter values.