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

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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 BertrandNash equilibrium, in the case of both linear and nonlinear 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 twodimensional system through a perioddoubling bifurcation. Moreover, by using numerical simulations (i.e., phase portraits, sensitive dependence on initial conditions and Lyapunov exponents), we find that a “quasiperiodic” route to chaos and a large gamma of strange attractors for the cases of both substitutability and complementarity can occur.
Item Type:  MPRA Paper 

Original Title:  The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited 
English Title:  The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited 
Language:  English 
Keywords:  Bifurcation; Chaos; Differentiated products; Duopoly; Price competition 
Subjects:  L  Industrial Organization > L1  Market Structure, Firm Strategy, and Market Performance > L13  Oligopoly and Other Imperfect Markets D  Microeconomics > D4  Market Structure and Pricing > D43  Oligopoly and Other Forms of Market Imperfection C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium 
Item ID:  33268 
Depositing User:  Luca Gori 
Date Deposited:  09. Sep 2011 14:51 
Last Modified:  13. Feb 2013 12:50 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/33268 