Differentiated Cournot duopoly game with fractional-order and its discretization

摘要: Fractional calculus provides powerful tool to build more realistic and accurate mathematical models in economic field. This paper aims explore a proposed fractional-order differentiated Cournot duopoly game its discretized game.,Conditions for existence uniqueness of the game’s solution are derived. The Nash equilibrium point local global stability obtained. Furthermore, analysis is investigated. effects on dynamics examined, along with other parameters game, via 2D bifurcation diagrams planes system’s acquired.,Theoretical numerical simulation results demonstrate rich variety interesting dynamical behaviors such as period-doubling Neimark–Sacker bifurcations, attractors’ crises addition chaotic attractors. demonstrated that can be lost by period doubling or bifurcations.,Oligopoly games pivotal modeling some substantial areas industrial organization, airline, banking, telecommunication companies, international trade also macroeconomic business cycles, innovation growth.,Although variants have attracted great interest among mathematicians economists since time proposition till present, memory continuous-time discrete-time not been addressed yet. To best author’s knowledge, this considered first attempt investigate problem game. In addition, studying oligopoly plays role investigation better understanding growth.