Nonlinear dynamics in a Cournot duopoly with relative profit delegation.

*(English)*Zbl 1258.91040Summary: This paper analyses the dynamics of a nonlinear Cournot duopoly with managerial delegation and homogeneous players. We assume that the owners of both firms hire a manager and delegate output decisions to him or her. Each manager receives a fixed salary plus a bonus based on relative (profit) performance. Managers of both firms may collude or compete. In cases of both collusion and a low degree of competition, we find that synchronised dynamics take place. However, when the degree of competition is high, the dynamics may undergo symmetry-breaking bifurcations, which can cause significant global phenomena. Specifically, there is on-off intermittency and blow-out bifurcations for several parameter values. In addition, several attractors may coexist. The global behaviour of the noninvertible map is investigated through studying a transverse Lyapunov exponent and the folding action of the critical curves of the map. These phenomena are impossible under profit maximisation.

##### MSC:

91A40 | Other game-theoretic models |

91A80 | Applications of game theory |

90B50 | Management decision making, including multiple objectives |

37N40 | Dynamical systems in optimization and economics |

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\textit{L. Fanti} et al., Chaos Solitons Fractals 45, No. 12, 1469--1478 (2012; Zbl 1258.91040)

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