The Entropy Complexity of an Asymmetric Dual-Channel Supply Chain with Probabilistic Selling

Considering consumers’ attitudes to risks for probabilistic products and probabilistic selling, this paper develops a dynamic Stackelberg game model of the supply chain considering the asymmetric dual-channel structure. Based on entropy theory and dynamic theory, we analyze and simulate the influences of decision variables and parameters on the stability and entropy of asymmetric dual-channel supply chain systems using bifurcation, entropy diagram, the parameter plot basin, attractor, etc. The results show that decision variables and parameters have great impacts on the stability of asymmetric dual-channel supply chains; the supply chain system will enter chaos through flip bifurcation or Neimark–Sacker bifurcation with the increase of the system entropy, and thus the system is more complex and falls into a chaotic state, with its entropy increased. The stability of the system can become robust with the increase of the probability that product [Formula: see text] becomes a probabilistic product, and it weakens with the increase of the risk preference of customers for probabilistic products and the relative bargaining power of the retailer. A manufacturer using the direct selling channel may obtain greater profit than one using traditional selling channels. Using the method of parameter adjustment and feedback control, the entropy of the supply chain system will decline, and the supply chain system will fall into a stable state. Therefore, in the actual market of probabilistic selling, the manufacturers and retailers should pay attention to the parameters and adjustment speed of prices and ensure the stability of the game process and the orderliness of the dual-channel supply chain.