Delay Stability of n -Firm Cournot Oligopolies

Akio Matsumoto and Ferenc Szidarovszky
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Akio Matsumoto: Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji, Tokyo 192-0393, Japan
Ferenc Szidarovszky: Department of Mathematics, Corvinus University, Fövám tér 8, 1093 Budapest, Hungary

Mathematics, 2020, vol. 8, issue 9, 1-19

Abstract: The dynamic behavior of n -firm oligopolies is examined without product differentiation and with linear price and cost functions. Continuous time scales are assumed with best response dynamics, in which case the equilibrium is asymptotically stable without delays. The firms are assumed to face both implementation and information delays. If the delays are equal, then the model is a single delay case, and the equilibrium is oscillatory stable if the delay is small, at the threshold stability is lost by Hopf bifurcation with cyclic behavior, and for larger delays, the trajectories show expanding cycles. In the case of the non-equal delays, the stability switching curves are constructed and the directions of stability switches are determined. In the case of growth rate dynamics, the local behavior of the trajectories is similar to that of the best response dynamics. Simulation studies verify and illustrate the theoretical findings.

Keywords: implementation delay; information delay; stability switching curve; Cournot oligopoly; growth rate dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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