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

Luciano Fanti and Luca Gori ()

Discussion Papers from Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy

Abstract: We revisit the study of the dynamics of a duopoly game a 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.

Keywords: Bifurcation; Chaos; Differentiated products; Duopoly; Price competition. (search for similar items in EconPapers)
JEL-codes: C62 D43 L13 (search for similar items in EconPapers)
Date: 2011-01-09
New Economics Papers: this item is included in nep-bec and nep-com
Note: ISSN 2039-1854
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Citations: View citations in EconPapers (3)

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Working Paper: The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:pie:dsedps:2011/120

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