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.
Highlights
Sarafopoulos et al DOIBounded rational players (sellers) update their strategies based on discrete-time periods using a local estimate of the marginal profit
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
The existence and the local stability of the equilibrium positions are studied; in Section 3, numerical simulations are used to verify the algebraic results of Section 2, we show the complex dynamics via graphing strange attractors, computing Lyapunov numbers, and sensitive dependence on initial conditions
Summary
Bounded rational players (sellers) update their strategies based on discrete-time periods using a local estimate of the marginal profit With such a local adjustment mechanism, the players are not requested to have a complete knowledge of the demand and cost functions [11] [13] [32] [33]. The paper is organized as follows: in Section 2, the dynamics of the duopoly game with homogeneous expectations, differentiated products, linear demand and asymmetric cost functions for two players are analyzed. Both players are set as bounded rationality.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
