×

Explicit stability zones for Cournot game with 3 and 4 competitors. (English) Zbl 0952.91003

Summary: The dynamical system of 3 and 4 competitors in a Cournot game is studied. The stability of its fixed points (Nash equilibria) are also investigated. The stable and unstable regions are explicitly shown. The bifurcation characteristics are found. Periodic orbits with different periods 7, 25, 18, 13, 17 etc., are detected in both cases. The study of these models is very rich in bifurcation phenomena.

MSC:

91A10 Noncooperative games
37G99 Local and nonlocal bifurcation theory for dynamical systems
37N40 Dynamical systems in optimization and economics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Puu, T., Chaos, 1, 573-581 (1991) · Zbl 0754.90015
[2] Puu, T., Chaos, Solitons and Fractals, 1996,7,; Puu, T., Chaos, Solitons and Fractals, 1996,7,
[3] Ahmed, E.; Agiza, H. N., Chaos, 9, 1513-1517 (1998)
[4] Cournot, A., Recherches sur les principes Mat. de la theo. theor. de la richesse; Cournot, A., Recherches sur les principes Mat. de la theo. theor. de la richesse
[5] Kopel, M., Chaos, Solitons, and Fractals, 1996,7,; Kopel, M., Chaos, Solitons, and Fractals, 1996,7, · Zbl 1080.91541
[6] Edelstien-Keshet, L., Math. Models in Biology; Edelstien-Keshet, L., Math. Models in Biology
[7] Drazin, P. G., Nonlinear system; Drazin, P. G., Nonlinear system
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.