Complexity in a Bertrand Duopoly Game with Heterogeneous Players and Differentiated Goods

Georges Sarafopoulos () and Kosmas Papadopoulos
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Georges Sarafopoulos: Democritus University of Thrace
Kosmas Papadopoulos: Democritus University of Thrace

A chapter in Economic and Financial Challenges for Eastern Europe, 2019, pp 15-26 from Springer

Abstract: Abstract In this paper we investigate the dynamics of a nonlinear discrete-time Bertrand duopoly game with differentiated goods. The players have heterogeneous expectations and the game is modeled with a system of two difference equations. Existence and stability of equilibria of this system are studied. We show that the model gives more complex chaotic and unpredictable trajectories as a consequence of change in the parameter of horizontal product differentiation. If this parameter is varied, the stability of Nash equilibrium is lost through period doubling bifurcations. The chaotic features are justified numerically via computing Lyapunov numbers and sensitive dependence on initial conditions.

Keywords: Bertrand duopoly game; Discrete dynamical system; Heterogeneous expectations; Stability; Chaotic behavior (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:prbchp:978-3-030-12169-3_2

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DOI: 10.1007/978-3-030-12169-3_2

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