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On a Bertrand Dynamic Game with Differentiated Goods, Heterogeneous Expectations and Asymmetric Cost Functions

In: Economic and Financial Challenges for Balkan and Eastern European Countries

Author

Listed:
  • Georges Sarafopoulos

    (Democritus University of Thrace)

  • Kosmas Papadopoulos

    (Democritus University of Thrace)

Abstract

The aim of this paper is to study the dynamics of a nonlinear Bertrand-type duopoly game with differentiated goods, linear demand and asymmetric cost functions. The game is modeled with a system of two difference equations. Existence and stability of equilibrium 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 speed of adjustment, which is followed by the bounded rational player, and in the parameter of product differentiation. A higher (lower) degree of player’s adjustment destabilizes (stabilize) the economy. Also, a higher or lower degree of product differentiation destabilizes the economy. The chaotic features are justified numerically via computing Lyapunov numbers, sensitive dependence on initial conditions, bifurcation diagrams and strange attractors.

Suggested Citation

  • Georges Sarafopoulos & Kosmas Papadopoulos, 2020. "On a Bertrand Dynamic Game with Differentiated Goods, Heterogeneous Expectations and Asymmetric Cost Functions," Springer Proceedings in Business and Economics, in: Marietta Janowicz-Lomott & Krzysztof Łyskawa & Persefoni Polychronidou & Anastasios Karasavvoglou (ed.), Economic and Financial Challenges for Balkan and Eastern European Countries, pages 223-241, Springer.
    • Handle: RePEc:spr:prbchp:978-3-030-39927-6_14
    DOI: 10.1007/978-3-030-39927-6_14
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