Open AccessStability switching and its directions in cournot duopoly game with three delays
Author(s) -
Akio Matsumoto,
Ferenc Szidarovszky
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021069
Subject(s) - cournot competition , duopoly , stability (learning theory) , eigenvalues and eigenvectors , equilibrium point , mathematics , point (geometry) , stability theory , mathematical economics , computer science , mathematical analysis , physics , geometry , differential equation , quantum mechanics , nonlinear system , machine learning
A three-delay duopoly is considered where the firms have identical implementation delays with different information delays. The equilibrium is locally asymptotically stable without delays however this stability is lost with increasing values of the delays. The stability properties of the equilibrium depend on the common implementation delay of the firms and on the sum of the two information delays. The stability switching curves are first analytically characterized and illustrated, and then the direction of the stability switching is determined at each point of the curves. The possibility of multiple pure imaginary eigenvalues is also discussed when the directions of the stability switches cannot be determined. Simulation examples illustrate the theoretical results.