Dynamic investigations in a duopoly game with price competition based on relative profit and profit maximization

This paper introduces an attempt to investigate the complex dynamics of a nonlinear duopoly game of players (firms) adopting prices as their decision variables. Two different models are introduced and studied in this paper. The models are built by following the traditional role in which players have limited information. The first model describes a competition between two firms whose main interest is to maximize their relative profits while the second is the classic Bertrand one with profit maximization. The paper shows several local and global analysis about the equilibrium points of each model. We show that classical Bertrand game studied in the second model gives better results than those obtained for the first one however the equilibrium in both models loses its stability via flip bifurcation only. (C) 2019 Elsevier B.V. All rights reserved.