SFB 303 Discussion Paper No. A - 048

Author: Davidson, Carl, and Raymond Deneckere
Title: Excess Capacity and Collusion
Abstract: Recently, there has been a tremendous resurgence of interest in oligopoly theory. The impetus for this resurgence stems from the consideration of dynamic aspects of oligopolistic markets. Two particular topics that have attracted a great deal of attention are the ability of firms to collude in a repeated game setting and the role that the timing of decisions - especially investment decisions - plays in determining oligopolistic outcomes.
In this paper, we develop and analyze a model which involves firms choosing a long term capacity level at the outset of the game. We do not allow firms to adjust this capacity level in subsequent periods. Given these initial capacity levels, firms then engage in a repeated game of price competition. Throughout this paper, we will assume that firms cannot collude in capacity even though they may be colluding in price. We assume that tacit collusion is the norm and that firms charge the maximum price that can be sustained in a collusive agreement, which is enforced by a threat (by all industry members) to permanently revert to the static Nash equilibrium as soon as anyone is caught cheating. The maximum sustainable price is defined to be the price that maximizes the "cartel welfare function" subject to the constraint that all firms find it optimal to abide by the agreement.
Formally, we characterize the subgame perfect Nash equilibria of a two-stage game in which firms first choose capacity levels and then, in a second stage, the maximum price that can be sustained in a collusive agreement. We find that all equilibria - except the ones in which firms mimic the static Cournot-Nash equilibrium - involve excess capacity. Moreover, the type and number of equilibria in this model depend upon two critical parameters - the cost of capacity and the discount rate. In order to perform meaningful comparative statics, we restrict our analysis to the set of equilibria that are Pareto undominated. We find that decreases in the level of collusion are always accompanied by decreases in the amount of excess capacity carried by the industry.
Creation-Date: February 1986
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