Location-Price Equilibria when Traditional Retailers Compete Against an Online Retailer.

We consider a location-then-price game where two traditional retailers compete with a location-irrelevant online retailer. We characterize the existing equilibria, and we show that in any possible equilibrium there is direct competition between the traditional retailers. Furthermore, the traditional retailers locate at neither a maximal nor minimal distance. In equilibrium, the price of the online retailer might be higher or lower than the price of the traditional retailers, depending on the relative competitiveness of the online retailer and the traditional retailers.

The Impacts of Green Innovation Input and Channel Service in a Dual-Channel Value Chain.

This paper constructs a dual-channel value chain composed of one altruistic manufacturer and one altruistic retailer, where the manufacturer makes green innovation input for green products and sells its green products to its customers through both the direct channel and the traditional channel, the retailer provides channel service for customers and sells green products through the traditional channel. We consider two scenarios in which the manufacturer and the retailer make decentralized and centralized decisions, respectively. We develop two dynamic game models for the two scenarios and analyze the dynamic behaviors of the two dynamic game models using bifurcation diagram, LLE (largest Lyapunov exponent) and attraction of basin, etc. We find that the stability region in decentralized decision model is greater than that of centralized decision, and narrow with increase of service value, green innovation input. In the decentralized decision model, the stability of the system decreases with the altruistic behavior increasing. With the price adjustment speed increasing, the dual-channel green value chain system enters into chaotic state through flip bifurcation or N-S bifurcation. In the stable state, the manufacturer and the retailer can obtain the maximum utility with the appropriate value of green innovation input. In the chaotic state, the utilities of the manufacturer and retailer are greatly affected and significantly reduced. This study will provide good guidance for sustainable development decision-making of dual-channel green value chain.

The Stability and Complexity Analysis of a Low-Carbon Supply Chain Considering Fairness Concern Behavior and Sales Service.

This paper studies a low-carbon dual-channel supply chain in which a manufacturer sells products through the direct channel and traditional channel, and a retailer sells products through the traditional channel. The manufacturer considers carbon emission reduction and has fairness concern behavior. The retailer provides sales service in the traditional channel and considers fairness concern behavior. The objective of this paper is to analyze the effects of different parameter values on the price stability and utility of the supply chain system emphatically using 2D bifurcation diagram, parameter plot basin, the basins of attraction, chaos attractor and sensitivity to the initial value, etc. The results find that the retailer's fairness concern behavior shrinks the stability of the supply chain system more than that of the manufacturer's fairness concern behavior. The system stability region decreases with the increase of carbon emission reduction level and the retailer's fairness concern. The customers' preference for the direct channel decreases the stable range of the direct channel, while it enlarges the stable range of the traditional channel. The supply chain system enters into chaos through flip bifurcation with the increase of price adjustment speed. In a stable state, the manufacture improving customer's preference for the direct channel and the retailer choosing the appropriate fairness concern level can achieve the maximum utility separately. In a chaotic state, the average utilities of the manufacturer and retailer all decline, while that of the retailer declines even more. By selecting appropriate control parameter, the low-carbon dual-channel supply chain system can return to a stable state from chaos again. The research of this paper is of great significance to price decisions of participants and supply chain operation management.

A Dynamic Price Game Model in a Low-Carbon, Closed-Loop Supply Chain Considering Return Rates and Fairness Concern Behaviors.

In this paper, we developed a dynamic price game model for a low-carbon, closed-loop supply chain system in which (1) the manufacturer had fairness concern and carbon emission reduction (CER) behaviors, and market share and profit maximization were their objectives, and (2) the retailer showed fairness concern behaviors in market competition and provided service input to reduce return rates. The retailer recycled old products from customers, and the manufacturer remanufactured the recycled old products. The effects of different parameter values on the stability and utility of the dynamic price game model were determined through analysis and numerical simulation. Results found that an increasing customer loyalty to the direct marketing channel decreased the stable region of the manufacturer's price adjustment and increase that of the retailer. The stable region of the system shrank with an increase of CER and the retailer's service level, which expanded with return rates. The dynamic system entered into chaos through flip bifurcation with the increase of price adjustment speed. In the chaotic state, the average utilities of the manufacturer and retailer all declined, while that of the retailer declined even more. Changes to parameter values had a great impact on the utilities of the manufacturer and retailer. By selecting appropriate control parameters, the dynamic system can return to a stable state from chaos again. The research of this paper is of great significance to participants' price decision-making and supply chain operation management.