Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

Abstract

This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm's preference is represented by a utility function that is derived from a constant elasticity of substitution (CES) production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics due to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations.

Evolution Dynamics of Agricultural Internet of Things Technology Promotion and Adoption in China

“…Ahmad and Marina [25] analyzed the existence of equilibrium for an exchange economy evolutionary model. Askar et al [26] investigated the Nash equilibrium and chaos fluctuations in a game model constructed by three competitive firms, and the firm's preference was derived from constant elasticity of substitution (CES) production function. Yu et al [27] constructed a 3D Hotelling price discrete dynamic model, analyzed the influence of important parameters on the model equilibrium, and described the chaotic behavior of the system through numerical simulation.…”

Equilibrium Further Studied for Combined System of Cournot and Bertrand: A Differential Approach

“…Quantity competition and price competition of oligopoly was debated for many years in an imperfectly competitive market. Some theorists [1][2][3][4][5][6][7] pointed out that the competitive equilibrium points, respectively, exist in the Cournot (quantity) model or Bertrand (price) model and compared the equilibrium with each other. Such as Singh and Vives first compared Cournot competition and Bertrand competition.…”

Analysis of a Four‐Firm Competition Based on a Generalized Bounded Rationality and Different Mechanisms

“…Rationality and heterogeneous expectations that may arise in models of economy have been studied in [11] by Hommes. Expectations mean that the behaviors adopted by a firm may be naive, rational, or local approximation mechanism. Those different types of expectations have been studied in literature (see [12][13][14][15][16][17][18]). In this paper, we adopt and focus on the bounded rationality approach and Puu's mechanism.…”