Georges Sarafopoulos¹, Evaggelos Drimpetas¹, Kosmas Papadopoulos^1*, Dimitrios Vezeris²

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¹ Department of Economics, Democritus University of Thrace, Komotini, Greece.
² Department of Electrical & Computer Engineering, Democritus University of Thrace, Xanthi, Greece.
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Abstract: This work presents the complexity that emerges in a Bertrand duopoly between two companies in the Greek oil market, one of which is semi-public and the other is private. The game uses linear demand functions for differentiated products from the existing literature and asymmetric cost functions that arose after approaches using the published financial reports of the two oil companies (Hellenic Petroleum and Motor Oil). The game is based on the assumption of homogeneous players who are characterized by bounded rationality and follow an adjustment mechanism. The players’ decisions for each time period are expressed by two difference equations. A dynamical analysis of the game’s discrete dynamical system is made by finding the equilibrium positions and studying their stability. Numerical simulations include bifurcation diagrams and strange attractors. Lyapunov numbers’ graphs and sensitivity analysis in initial conditions prove the algebraic results and reveal the complexity and chaotic behavior of the system focusing on the two parameters k₁ and k₂ (speed of adjustment for each player). The d-Backtest method is applied through which an attempt is made to control the chaos that appears outside the stability space in order to return to the locally asymptotically stable Nash equilibrium for the system.

Keywords: Duopoly Game, Discrete Dynamical System, Nash Equilibrium, Stability, Bifurcation, Chaotic Behavior, d-Backtest Method

Cite this paper: Sarafopoulos, G. , Drimpetas, E. , Papadopoulos, K. and Vezeris, D. (2021) Dynamics of a Bertrand Duopoly Game of the Greek Oil Market and Application of the d-Backtest Method. Applied Mathematics, 12, 1097-1117. doi: 10.4236/am.2021.1211070.

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