The Complex Dynamics of Bertrand-Stackelberg Pricing Models in a Risk-Averse Supply Chain

We construct dynamic Bertrand-Stackelberg pricing models including two manufacturers and a common retailer in a risk-averse supply chain with the uncertain demand. The risk-averse supply chain follows these strategies: Bertrand game between the two manufacturers and Stackelberg game between the manufacturer and the retailer. We study the effect of the price adjustment speed, the risk preference, and the uncertain demand on the stability of the risk-averse supply chain using bifurcation, power spectrum, attractor, and so forth. It is observed that there exists slip bifurcation when the price adjustment speed across some critical value, the stable region, and total profit of the risk-averse supply chain will increase with increase of R-M1 and decrease with increase of sigma. The profit of the supply chain and the two manufacturers will decrease and the weaker (retailer) is a beneficiary when the supply chain is in chaos. The fluctuation in the supply chain can be gradually controlled by the control of the price adjustment speed.