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Stability Analysis of a Master–Slave Cournot Triopoly Model: The Effects of Cross-Diffusion

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Titel: Stability Analysis of a Master–Slave Cournot Triopoly Model: The Effects of Cross-Diffusion
Autoren: Maria Francesca Carfora, Isabella Torcicollo
Quelle: Axioms, Vol 14, Iss 7, p 540 (2025)
Verlagsinformationen: MDPI AG, 2025.
Publikationsjahr: 2025
Bestand: LCC:Mathematics
Schlagwörter: Turing instability, Turing pattern formation, reaction–diffusion system, Mathematics, QA1-939
Beschreibung: A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms’ decisions about production levels play a crucial role in determining overall market output. Compared to duopoly models, oligopolies with more than two firms have received relatively less attention in the literature. Nevertheless, triopoly models are more reflective of real-world market conditions, even though analyzing their dynamics remains a complex challenge. A reaction–diffusion system of PDEs generalizing a nonlinear triopoly model describing a master–slave Cournot game is introduced. The effect of diffusion on the stability of Nash equilibrium is investigated. Self-diffusion alone cannot induce Turing pattern formation. In fact, linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. The conditions for the onset of cross-diffusion-driven instability are obtained via linear stability analysis, and the formation of several Turing patterns is investigated through numerical simulations.
Publikationsart: article
Dateibeschreibung: electronic resource
Sprache: English
ISSN: 2075-1680
Relation: https://www.mdpi.com/2075-1680/14/7/540; https://doaj.org/toc/2075-1680
DOI: 10.3390/axioms14070540
Zugangs-URL: https://doaj.org/article/2daad5396b1a4dd0b41b4bf3fd56deab
Dokumentencode: edsdoj.2daad5396b1a4dd0b41b4bf3fd56deab
Datenbank: Directory of Open Access Journals
Beschreibung
Abstract:A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms’ decisions about production levels play a crucial role in determining overall market output. Compared to duopoly models, oligopolies with more than two firms have received relatively less attention in the literature. Nevertheless, triopoly models are more reflective of real-world market conditions, even though analyzing their dynamics remains a complex challenge. A reaction–diffusion system of PDEs generalizing a nonlinear triopoly model describing a master–slave Cournot game is introduced. The effect of diffusion on the stability of Nash equilibrium is investigated. Self-diffusion alone cannot induce Turing pattern formation. In fact, linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. The conditions for the onset of cross-diffusion-driven instability are obtained via linear stability analysis, and the formation of several Turing patterns is investigated through numerical simulations.
ISSN:20751680
DOI:10.3390/axioms14070540