The “Win-Continue, Lose-Reverse” Rule in Cournot Oligopolies: Robustness of Collusive Outcomes

The so-called “Win-Continue, Lose-Reverse” (WCLR) rule is a simple procedure that can be used to choose a value for any numeric variable (e.g. setting a production level to maximise profit). The rule dictates that one should evaluate the consequences of the last adjustment made to the value (e.g. an increase or a decrease in production), and keep on changing the value in the same direction if the adjustment led to an improvement (e.g. if it led to greater profits), or reverse the direction of change otherwise. Somewhat surprisingly, this simple rule has been shown to lead to collusive outcomes in Cournot oligopolies, even though its application requires no information whatsoever about the choices made by any competing firms or about their results. Firms applying the WCLR rule need only know whether the last change in their own production turned out to be profitable or not; thus, there is no room for explicit coordination or collusion. In this paper we show that the convergence of the WCLR rule towards collusive outcomes can be very sensitive to small independent perturbations in the cost functions and in the income functions of the firms. These perturbations typically push the process towards the Cournot–Nash equilibrium of the one-shot game. Importantly, the destabilizing power of the independent perturbations is mainly due to the fact that they create miscoordination among the firms. In fact, if there is correlation between the perturbations, their impact on the dynamics of the model is not so dramatic.