Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game

Sameh S Askar and Abdulrahman Al-Khedhairi
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Sameh S Askar: Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
Abdulrahman Al-Khedhairi: Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Mathematics, 2020, vol. 8, issue 9, 1-16

Abstract: The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game’s dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained.

Keywords: Bischi–Naimzada game; bounded rationality; flip bifurcation; critical curves; basin of attraction; noninvertible map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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