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

  • Georges SarafopoulosEmail author
  • Kosmas Papadopoulos
Conference paper
Part of the Springer Proceedings in Business and Economics book series (SPBE)


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.


Bertrand duopoly game Discrete dynamical system Heterogeneous expectations Stability Chaotic behavior 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of EconomicsDemocritus University of ThraceKomotiniGreece

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