A competition of duopoly game whose players are public: Dynamic investigations

Based on a generalized nonlinear price function and consumer surplus, a Cournot duopoly game whose players want to maximize their profits and social welfare is introduced in this paper. Just like studies in literature, the game is modeled by a nonlinear two-dimensional discrete map. Due to the general price function, the dynamics for the model such as local and global dynamic behaviors, synchronization and multi-stability are investigated at some special cases. The studies and the formation of game in this paper generalize other studies in literature. The general forms of the equilibrium points including Nash one are calculated. Analytically, the conditions of stability for those points are investigated. Focusing on Nash point and its dynamics, it is confirmed that the map's manifold can be studied using a one-dimensional map that is similar to the famous logistic map. It is confirmed that the game's map is noninvertible and belongs to the Z(4) - Z(2) - Z(0) type. The global bifurcation is analyzed using critical curves for some attracting sets and chaotic attractors. The symmetry of the game makes the diagonal line form an invariant set and hence synchronization is discussed. (C) 2022 Elsevier B.V. All rights reserved.