Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost

In this paper, some mathematical properties and dynamic investigations of a Cournot–Bertrand duopoly game using a computed nonlinear cost are studied. The game is repeated and its evolution is presented by noninvertible map. The fixed points for this map are calculated and their stability conditions...

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Bibliographic Details
Published in:	Complexity (New York, N.Y.) Vol. 2024; pp. 1 - 15
Main Authors:	Askar, S. S., Alshamrani, Ahmed M.
Format:	Journal Article
Language:	English
Published:	Hoboken Hindawi 2024 Hindawi Limited Hindawi-Wiley
Subjects:	Behavior Bifurcations Competition Computation Cost analysis Duopoly Equilibrium Fixed points (mathematics) Game theory Games Prices Profits Rationality
Online Access:	Get full text
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Summary:	In this paper, some mathematical properties and dynamic investigations of a Cournot–Bertrand duopoly game using a computed nonlinear cost are studied. The game is repeated and its evolution is presented by noninvertible map. The fixed points for this map are calculated and their stability conditions are discussed. One of those fixed points is Nash equilibrium, and the discussion shows that it can be unstable through flip and Neimark–Sacker bifurcation. The invariant manifold for the game’s map is analyzed. Furthermore, the case when both competing firms are independent is investigated. Due to unsymmetrical structure of the game’s map, global analysis gives rise to complicated basin of attraction for some attracting sets. The topological structure for these basins of attraction shows that escaping (infeasible) domain for some attracting sets becomes unconnected and the rise of holes is obtained. This confirms the existence of contact bifurcation.
ISSN:	1076-2787 1099-0526
DOI:	10.1155/2024/5594918