Delay Cournot Duopoly Game with Gradient Adjustment: Berezowski Transition from a Discrete Model to a Continuous Model

Akio Matsumoto, Ferenc Szidarovszky and Keiko Nakayama
Additional contact information
Akio Matsumoto: Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji, Tokyo 192-0393, Japan
Ferenc Szidarovszky: Department of Mathematics, Corvinus University, Fovám tér 8, 1093 Budapest, Hungary
Keiko Nakayama: Department of Economics, Chukyo University, 101-2, Yagoto Honmachi, Showa, Hagoya 466-8666, Japan

Mathematics, 2020, vol. 9, issue 1, 1-19

Abstract: This paper investigates the asymptotical behavior of the equilibrium of linear classical duopolies by reconsidering the two-delay model with two different positive delays. In a two-dimensional analysis, the stability switching curves were first analytically determined. Numerical studies verified and illustrated the theoretical results. In the sensitivity analysis it was demonstrated that the inertia coefficient has a twofold effect: enlarges the stability region as well as simplifies the complicated dynamics with period-halving cascade. In contrary, the adjustment speed contracts the stability region and complicates simple dynamics with period-doubling bifurcation. In addition, for various values of τ 1 and τ 2 , a wide variety of dynamics appears ranging from simple cycle via a Hopf bifurcation to chaotic oscillations.

Keywords: two delays; Cournot duopoly; gradient dynamics; stability switching curve; bifurcation diagram; complex dynamics (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:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/1/32/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/1/32/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2020:i:1:p:32-:d:468104

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().