Is capital a collusion device? (Q1865169)

The authors study an infinitely repeated model of capital capacity choices and quantitycompetition of two firms producing a homogeneous good. It is closely related to a class of earlier investigated models focusing on the relationship between the ability of an oligopolistic industry to sustain tacit collusion and the capital structure of the firms. The paper can also be included to a vast literature on the role of commitment in strategic situations. It starts with the specification of two similar profit functions for the two players (firms) which represent the present values of expected profits and involve among others a capital intensity parameter \(u\) and the interest rate \(r\). The latter stands for the period capital cost and determines the discount factor \(1/1+r\). In each period, the firms select their capacities and outputs. Since any deviation from a cooperation triggers a punishment, each firm compares the potential gain in profits in the period of defection with the discounted loss in profits during the punishment period. If the punishment is sufficiently painful, i.e., the loss in profits are discounted by means of a small enough interest rate \(r\), the firms will not deviate and the cooperation is proved to be a subgame perfect equilibrium. The authors first characterize grim strategies to conclude that in the reversible capital case, they correspond to Cournot-Nash strategies. On the other hand, in the irreversible case, the firms enter the punishment phase with different capacity levels, and then grim strategies correspond to one-period Cournot choices with different initial irreversible capacity levels. It is shown that in the irreversible case the incentive to deviate from the cooperation remains higher. Besides, for each initial capital intensity \(u\), there is an interval \([0,r^*]\) comprising such interest rates \(r\) for which collusion is a stable outcome, and the function \(r^*(u)\) is decreasing to zero, meaning that implicit collusion becomes practically impossible. It is shown that the value of commitment can be negative for all players. In contrast to the case of reversible capital, the set of interest rates for which collusion is supported depends on the amount of capital that is necessary to produce an output unit.