The "Win-Continue, Lose-Reverse" rule in Cournot oligopolies

Segismundo S. Izquierdo & Luis R. Izquierdo


To use WC-LR-Cournot, you will have to install NetLogo 5.3.1 (free and open source) and download the model itself. Unzip the downloaded file and click on wc-lr-cournot.nlogo


WC-LR-Cournot is a model designed to analyse the Win-Continue, Lose-Reverse rule in Cournot oligopolies. This section gives an informal and brief overview of WC-LR-Cournot. We use bold red italicised arial font to denote parameters (i.e. variables that can be set by the user). Any parameter value can be changed at runtime, with immediate effect on the dynamics of the model.

In WC-LR-Cournot, there are num-firms firms which provide a homogeneous good or service and have to choose their production level qi. The market price p depends on the total amount SUMi(qi) produced by the firms, and -in principle- it is the same for all firms. (The model can be parameterised so there can be small differences among the prices that each company receives for its products.) The process advances in discrete time steps and at every time step the companies have to simultaneously choose whether to increase or decrease their production level qi. The decision rule considered here can be simply stated as: repeat your last action (i.e. an increase or a decrease in production) if your profits have grown; otherwise, choose the opposite action. This simple rule has been named "Win-Continue, Lose-Reverse" (WCLR) by Huck et al. (2003), who conducted a thorough study of its convergence properties in symmetric Cournot oligopolies.


This section explains the formal model that WC-LR-Cournot implements. The information provided here should suffice to re-implement the same formal model in any sophisticated enough modelling platform.

The considered model is a Cournot duopoly in which at every time step t (t = 0, 1, ...) each company i (i = 1, 2, ... ,num-firms) chooses a production level or quantity [qi]t. In principle, the market price [p]t is the same for all companies and it depends on the total quantity produced by all firms, according to the following formula:

[p]t = p0 - a·SUMi([qi]t).

The amount [qi]t is produced on period t with the cost function C(q):

C(q) = c0 + c1·q + c2·q2.

The profit for each company on period t is

[πi]t = [pi]t·[qi]t - C([qi]t).

Incremental values are naturally defined as [Δπi]t := [πi]t - [πi]t-1, and initial values at time step 0 are [Δπi]0 = 0, and [Δqi]0 = 0.

Let us also define [si]t := SIGN([Δqi]t·[Δπi]t). Note that [si]t is equal to +1 if the last changes in [qi]t and [πi]t took place in the same direction, and [si]t is equal to -1 if such changes went in opposite directions.

For each company i, the production levels are calculated as [qi]t+1 = MAX([qi]t + [Δqi]t+1, 0), starting with a random initial positive production level [qi]0 at time step 0. (To be precise, [qi]0 is a random multiple of step in the range [0, (p0 / (a * num-firms)].) The decision rule WCLR used to calculate the production increments [Δqi]t+1 is implemented as follows:

WCLR Rule:


It is also assumed that the process includes three types of "noise":








wc-lr-cournot is a model designed to analyse the "Win-Continue, Lose-Reverse" rule in Cournot oligopolies.
Copyright (C) 2014 Segismundo S. Izquierdo & Luis R. Izquierdo

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Contact information:
Segismundo S. Izquierdo
University of Valladolid, Spain.


This program has been designed and implemented by Segismundo S. Izquierdo & Luis R. Izquierdo.