A note on a fractional Cournot-type model - Corrêa, Matheus Madeira (2024)
In this contribution, we analyze the memory effect associated with fractional derivatives in a Cournot-type oligopoly model. Such an analysis will be made from the comparison of the solutions of a duopoly with fractional derivatives of different orders. We show that the firm that has more memory on the competition, given by the fractional derivative, will have advantages over its competitor in the long run. Moreover, we show that the choices of fractional derivatives αj ∈ (0,3/5) for both firms j = 1,2 will result in advantages in profit compared to the profit of firms without memory.