The rise of complex phenomena in Cournot duopoly games due to demand functions without inflection points

• Cournot duopoly games based on non-linear demand functions that have no inflection points are proposed.
• The bounded rationality and Puu’s incomplete information approach are used to construct the dynamical systems.
• Complex phenomena such as stability, bifurcation and chaos are detected and studied.

In this paper, we propose Cournot duopoly games where quantity-setting firms use non-linear demand functions that have no inflection points. Two different kinds of repeated games are introduced based on rationality process of firms and Puu’s incomplete approach. First, a model of two rational firms that are in competition and produce homogenous commodities is introduced. The equilibrium points of this model are obtained and their dynamical characteristics such as stability, bifurcation and chaos are investigated. By using rationality process firms do not need to solve any optimization problem but they adjust their production based on estimation of the marginal profit. Using Puu’s incomplete information approach a new model is introduced. As in the first model, the equilibrium points are obtained and their dynamical characteristics are investigated. By using Puu’s approach firms only need to know their profits and the quantities produced in the past two times. We compare the properties of the two models under the two approaches. The paper extends and generalizes the results of other authors that consider similar processes.