Dynamics in linear Cournot duopolies with two time delays.

*(English)*Zbl 1282.91202Summary: Linear differential duopolies are constructed with continuous time scales, constant coefficients and two types of information delays: fixed and continuously distributed time delays. System dynamics are considered with delays in the diagonal terms. By analyzing the associated characteristic equations, it is found that the stability is lost when the lengths of delays cross some critical values. Then it is shown that the destabilizing effect caused by the fixed delays is stronger than the destabilizing effect of the distributed delays having exponentially-declining weighting function. It is further demonstrated that the strength of the destabilizing effect is reversed if the distributed delay has a bell-shaped weighting function.

##### MSC:

91B55 | Economic dynamics |

91B26 | Auctions, bargaining, bidding and selling, and other market models |

91B54 | Special types of economic markets (including Cournot, Bertrand) |

37N40 | Dynamical systems in optimization and economics |

##### Keywords:

Cournot competition; fixed time delay; continuously distributed time delay; two delays; stability switches
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\textit{A. Matsumoto} et al., Comput. Econ. 38, No. 3, 311--327 (2011; Zbl 1282.91202)

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##### References:

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