This article is cited in 2 papers

Control in Social Economic Systems

Convergence conditions for the dynamics of reflexive collective behavior in a Cournot oligopoly model under incomplete information

G. I. Algazin, D. G. Algazina

Altai State University, Barnaul, Russia

Abstract: This paper considers a Cournot oligopoly model with an arbitrary number of rational agents under incomplete information in the classical case (linear cost and demand functions). Within the dynamic reflexive collective behavior model, at each time instant each agent adjusts his output, taking a step towards the maximum profit under the expected choice of the competitors. Convergence conditions to a Cournot–Nash equilibrium are analyzed using the errors transition matrices of the dynamics. Restrictions on the ranges of agents' steps are imposed and their effect on the convergence properties of the dynamics is demonstrated. Finally, a method is proposed to determine the maximum step ranges ensuring the convergent dynamics of collective behavior for an arbitrary number of agents.

Keywords: Cournot oligopoly, incomplete awareness, reflexive collective behavior, errors transition matrix, step ranges, convergence conditions.

Presented by the member of Editorial Board: D. A. Novikov

Received: 07.10.2022
Revised: 02.02.2023
Accepted: 15.02.2023

DOI: 10.31857/S0005231023050045

 English version: Automation and Remote Control, 2023, 84:5, 486–496