The dynamics of Bertrand model with bounded rationality

The dynamics of a Bertrand duopoly with differentiated products: Synchronization, intermittency and global dynamics

“…The present paper revisits the study of the dynamics of a nonlinear duopoly à la Bertrand [6] with horizontal product differentiation analyzed by Zhang et al [35]. 1 Given the importance of product differentiation in the current industrial organization literature (see [31]), different from Zhang et al [35], in this paper we develop a model with sound microeconomic foundations that determine the demand of differentiated products faced by each firm on the market.…”

“…We study the dynamics of a duopoly game à la Bertrand with horizontal product differentiation as proposed by Zhang et al (2009) [35] by introducing opportune microeconomic foundations. The final model is described by a two-dimensional non-invertible discrete time dynamic system T. We show that synchronized dynamics occurs along the invariant diagonal being T symmetric; furthermore, we show that when considering the transverse stability, intermittency phenomena are exhibited.…”

“…1 Given the importance of product differentiation in the current industrial organization literature (see [31]), different from Zhang et al [35], in this paper we develop a model with sound microeconomic foundations that determine the demand of differentiated products faced by each firm on the market. In this way, by using the degree of product differentiation as the key parameter some dynamic behaviors, which are of importance in both mathematics and economics, are discovered.…”

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

“…They have discussed that the degree of products differentiation had a major impact on the sale quantity and price. Bertrand duopoly model was investigated by Zhang et al [36] depending on the price competition with bounded rationality. Peng [37] and Peng et al [38] have introduced other Bertrand models in order to study and assess complexity of the model.…”

Multi-Team Bertrand Game with Heterogeneous Players

“…The standard static Bertrand game has been studied in [12]. A duopoly Bertrand game with bounded rationality is studied in [13]. Multi-team bertrand game is studied in [14] with two teams but the second team consists of one player.…”