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

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 Balkan and Eastern European Countries, 2020, pp 223-241 from Springer

Abstract: 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.

Keywords: Bertrand duopoly game; Discrete dynamical system; Heterogeneous expectations; Asymmetric costs; Stability; Chaotic behavior (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:prbchp:978-3-030-39927-6_14

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DOI: 10.1007/978-3-030-39927-6_14

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