Triopoly Cournot–Bertrand Game Based on Fractional Bounded Rationality: Static and Dynamic Investigations

A triopoly game is introduced to study the competition among three frms in a single market, each operating in an oligopolistic market. Our study is concerned with a static model in which the market has taxes and a quadratic cost function in quantity. In the static system we employ, known as Cournot-Bertrand, one frm’s output depends on quantity, while the other frms’ outputs depend on price. In the frst part of this paper, we study the existence of the Nash equilibrium and its condition of stability for the static mixed model. In the second part of this paper, we modify the standard bounded rationality to fractional bounded rationality of discrete dynamical systems that have increasing taxes according to quantities based on the Egyptian market. Finally, we present a numerical study of the dynamical system, demonstrating that a small degree of memory enhances system stability.