Complexity analysis of dual-channel game model with different managers’ business objectives

• Dual-channel model with different managers’ business objectives is established.
• A fiercer competition tends to stabilize the Nash equilibrium point.
• The optimal strategy is in the stable region of Nash equilibrium point.
• We use the parameters adjustment method to control the economic system.
• Unstable behavior in economic system often cause an unfavorable outcome.

This paper considers dual-channel game model with bounded rationality, using the theory of bifurcations of dynamical system. The business objectives of retailers are assumed to be different, which is closer to reality than previous studies. We study the local stable region of Nash equilibrium point and find that business objectives can expand the stable region and play an important role in price strategy. One interesting finding is that a fiercer competition tends to stabilize the Nash equilibrium. Simulation shows the complex behavior of two dimensional dynamic system, we find period doubling bifurcation and chaos phenomenon. We measure performances of the model in different period by using the index of average profit. The results show that unstable behavior in economic system is often an unfavorable outcome. So this paper discusses the application of adaptive adjustment mechanism when the model exhibits chaotic behavior and then allows the retailers to eliminate the negative effects.