Fractional calculus applied to the Cournot-type adjustment model

In this contribution, we propose the incorporation of memory in a Cournot-type model for the process of adjusting the production of firms in a duopoly market, through the calculation of fractional order. Under the simplifying assumption that the inverse demand and costs of firms are affine functions of the quantities produced, we show numerically some conditions on memory (fractional derivative order) and on the speed of the adjustment process, so that the model proposed converges to Cournot's generalized stationary points. Under these assumptions, we show that the firm that has more memory obtains greater profit.