Nonlinear dynamics in a Cournot duopoly with relative profit delegation
The present study analyses the dynamics of a nonlinear Cournot duopoly with managerial delegation and bounded rational players. Problems concerning strategic delegation (based on relative performance evaluations) have recently received in depth attention in both the theoretical and empirical industrial economics literatures. In this paper, we take a dynamic view of this problem and assume that the owners of both firms hire a manager and delegate output decisions to him. Each manager receives a fixed salary plus a bonus offered in a publicly observable contract. The bonus entitled to the manager hired by the owner of every firm is based on relative (profit) performance. Managers of both firms may collude or compete. In such a context, we find, in either cases of collusion and low degree of competition, that synchronised dynamics takes place. However, when the degree of competition increases the dynamics can undergo symmetry-breaking bifurcations that may cause relevant global phenomena. In particular, on-off intermittency and blow-out bifurcations are observed for several parameter values. Moreover, coexistence of attractors may also occur. The global behaviour of the noninvertible map is investigated through the study of the transverse Lyapunov exponent and the folding action of the critical curves of the map. These phenomena are impossible under profit maximisation.
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