Nonlinear dynamics in a Cournot duopoly with relative profit delegation

Abstract

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.

Local and global dynamics in a duopoly with price competition and market share delegation

“…Similar events are found by Bischi et al [10] under profit-maximizing quantity-setting firms but only when they are heterogeneous (asymmetric map). From a mathematical point of view, this holds because -unlike Bischi et al [10] -the two-dimensional map that characterizes the Cournot duopoly with relative profit delegation of Fanti et al [18] contains a parameter (i.e., the relative managers' attitude in their objective functions) that weights the mixed term without affecting the pure quadratic term.…”

“…The present paper is connected with the work of Fanti et al [18], that has developed a nonlinear Cournot duopoly with quantity setting firms and managerial incentive contracts based on relative profit delegation. Despite the assumption of homogeneous players (symmetric system), they have shown that an increase in the degree of competition between managers may be a source of on-off intermittency, blow-out phenomena and multistability.…”

“…Following Bischi et al [10] and Fanti et al [18,19], we assume that both players have limited information regarding manager bonuses (no knowledge of the market). However, they follow an adjustment process based on local estimates of the marginal bonus to overcome this informational lacuna (for similar mechanisms see [9] or [7] with regard to a discrete time model, and [16] with regard to a continuous time model).…”

Evolutionary Games in the Agricultural Product Quality and Safety Information System: A Multiagent Simulation Approach

“…These researches show that the adaptive parameters' variation would change systematic stability but would not lead the system to chaotic states; however, the boundedrationality parameters might cause the systematic chaos. Fanti et al [7] discussed the dynamics of a nonlinear Cournot duopoly with managerial delegation. Su et al [8] applied a multiple test methodology to identify the nonlinear, fractal, and chaotic characteristics in the agricultural price system.…”

Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities

“…Dynamic Cournot game models were discussed in the following references, in which players used output as the decision variable. Fanti et al [10] analyzed the dynamics of a nonlinear Cournot duopoly with managerial delegation. Ma and Guo [11] studied the estimation accuracy by assuming that the second player makes his estimation based on recursive least-square (RLS) algorithm and compared the profit in two-period decision-making process with that in oneperiod decision-making process.…”