The so-called “Win-Continue, Lose-Reverse” (WCLR) rule is a simple iterative procedure that can be used to choose a value for any numeric variable (e.g., setting a price or a production level). The rule dictates that one should evaluate the effect on profits of the last adjustment made to the value (e.g., a price variation), and keep on changing the value in the same direction if the adjustment 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 about the other firms’ profits or choices. In this paper, we show that the convergence of the WCLR rule toward collusive outcomes can be very sensitive to small independent perturbations in the cost functions or in the income functions of the firms. These perturbations typically push the process toward the Nash equilibrium of the one-shot game. We also explore the behavior of WCLR against other strategies and demonstrate that WCLR is easily exploitable. We then conduct a similar analysis of the WCLR rule in a differentiated Bertrand model, where firms compete in prices.
A General Cournot-Bertrand Model with Homogeneous Goods