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.
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Sarafopoulos, G., Papadopoulos, K. (2020). On a Bertrand Dynamic Game with Differentiated Goods, Heterogeneous Expectations and Asymmetric Cost Functions. In: Janowicz-Lomott, M., Łyskawa, K., Polychronidou, P., Karasavvoglou, A. (eds) Economic and Financial Challenges for Balkan and Eastern European Countries. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-39927-6_14
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