The complexion of dynamic duopoly game with horizontal differentiated products

• Published in: Economic modelling 2014-08, Vol.41, p.289-297
• Main Authors: Yu, Weisheng, Yu, Yu
• Format: Article
• Language: English
• Subjects: Chaos; Competition; Duopoly; Duopoly game; Economic theory; Equilibrium; Game theory; Hotelling model; Marketing; Price competition; Pricing policies; Product differentiation; Rational expectations; Stability; Studies; The degree of product differentiation
• ISSN: 0264-9993; 1873-6122
• DOI: 10.1016/j.econmod.2014.05.024

In this paper, firms are considered on the hypothesis of having incomplete rationality expectation and incomplete information of the market to get the dynamic development of price competition behavior in the Hotelling model (Hotelling, 1929). Under the assumption of the heterogeneous expectations of two firms, we have observed that the Nash equilibrium price can be a dynamic equilibrium to realize when the speed of price adjustment is lower. However, the numerical simulation shows that the system may present a periodic and chaotic status when the speed of price adjustment is higher. The effect of the degree of horizontal differentiation on the stability of Nash equilibrium of the system is also discussed. We have a different conclusion from Lucino Fanti and Luca Gori's (2012); that is the greater the degree of product horizontal differentiation is, the more stable the Nash equilibrium of the system is. •We construct dynamic models on the basis of differentiated products.•The increase of degree of product differentiation increases the stability of the system.•Chaos occurs through a flip bifurcation.•We consider duopolists as bounded rational players and naïve rational players.•Strange attractors and the sensitivity of initial value are also shown in this article.