Delayed Feedback Chaos Control on a Cournot Game with Relative Profit Maximization

Kosmas Papadopoulos, Georges Sarafopoulos and Evangelos Ioannidis ()
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Kosmas Papadopoulos: Department of Economics, Democritus University of Thrace, 69100 Komotini, Greece
Georges Sarafopoulos: Department of Economics, Democritus University of Thrace, 69100 Komotini, Greece
Evangelos Ioannidis: Department of Economics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

Mathematics, 2025, vol. 13, issue 15, 1-18

Abstract: This article concerns a Cournot duopoly game with homogeneous expectations. The cost functions of the two players are assumed to be asymmetric to capture possible asymmetries in firms’ technologies or firms’ input costs. Large values of the speed of adjustment of the players destabilize the Nash Equilibrium (N.E.) and cause the appearance of a chaotic trajectory in the Discrete Dynamical System (D.D.S.) . The scope of this article is to control the chaotic dynamics that appear outside the stability field, assuming asymmetric cost functions of the two players. Specifically, one player uses linear costs, while the other uses nonlinear costs ( quadratic or cubic ). The cubic cost functions are widely used in the Economic Dispatch Problem . The delayed feedback control method is applied by introducing a new control parameter at the D.D.S. It is shown that larger values of the control parameter keep the N.E. locally asymptotically stable even for higher values of the speed of adjustment.

Keywords: Cournot duopoly game; discrete dynamical system; bifurcation diagram; chaotic attractor; Lyapunov numbers; complexity; chaotic behavior; delayed feedback control; chaos control; cubic cost function; non-convex cost function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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