Collusive Capacity

It is widely believed that cartels with too many members are destined to fail. The standard argument is that as the number of cartel members increases, shares of collusive profit diminish relative to deviation profits. We show that this argument is built on unreasonable assumptions about plant capacity. We add plant capacity choices to an otherwise standard dynamic oligopoly game, and we analyze the feasibility of a collusive strategy in which each firm chooses plant capacity equal to its static Nash output level, produces an equal share of monopoly output, and uses Nash reversion to punish deviations. Our main results are constructive. We first derive a uniform upper-bound on the minimum discount factor needed for collusion based on the ratio of collusive to monopolistic profits. We then prove that as the number of firms goes to infinity, our collusive strategy profile is an equilibrium as long as the discount factor is below 0.63. Thus, collusion is robust to the number of firms when capacity is chosen pro-collusively. Finally, we use the rho-concavity concept for classifying demand to obtain sharper bounds based on demand primitives.