Munich Personal RePEc Archive

The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited

Fanti, Luciano and Gori, Luca (2011): The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited.

[img]
Preview
PDF
MPRA_paper_33268.pdf

Download (730Kb) | Preview

Abstract

We revisit the study of the dynamics of a duopoly game à la Bertrand with horizontal product differentiation and bounded rational firms analysed by Zhang et al. (2009), (Zhang, J., Da, Q., Wang, Y., 2009. The dynamics of Bertrand model with bounded rationality. Chaos, Solitons and Fractals 39, 2048–2055), by introducing sound microeconomic foundations. We study how an increase in the relative degree of product differentiation affects the stability of the unique positive Bertrand-Nash equilibrium, in the case of both linear and non-linear costs. We show that an increase in either the degree of substitutability or complementarity between goods of different variety may destabilise the equilibrium of the two-dimensional system through a period-doubling bifurcation. Moreover, by using numerical simulations (i.e., phase portraits, sensitive dependence on initial conditions and Lyapunov exponents), we find that a “quasi-periodic” route to chaos and a large gamma of strange attractors for the cases of both substitutability and complementarity can occur.

UB_LMU-Logo
MPRA is a RePEc service hosted by
the Munich University Library in Germany.