Price Game Model Research Articles

Stability Analysis and Chaos Control of Recycling Price Game Model for Manufacturers and Retailers

With application of nonlinear theory, this paper makes study on the long‐term competition in a recycling price game model by manufacturers and retailers. The paper makes analysis on the local stability of the Nash equilibrium point and gives the corresponding stable region. It has been found that the stability of the whole system would be significantly impacted by the following factors which include adjustment speed of the recycling price, the proportion of recycled products by channels, the sensitivity of consumers for the recycling price, and the price cross‐elasticity between two channels. By means of the simulation technology, the complexity of the recycling price in the system in the long‐term competition has been demonstrated. Owing to the change of parameters, bifurcation, chaos, and other phenomena would appear in the system. When the system is becoming chaotic, the profit of the whole system decreased. All these show that the operational efficiency for the whole system will be impaired by the chaos. Effective chaotic control of the system will be realized by the use of the parameter adaptation method.

Research on Dynamic Game Model and Application of China’s Imported Soybean Price in the Context of China‐US Economic and Trade Friction

China’s soybean price fluctuates due to the current economic and trade frictions between China and the United States. Brazil and the United States are regarded as two oligarchs in China’s soybean import market. A dynamic price game model is established, and price elasticity parameters are estimated by using statistical data and Rotterdam model. The stability of Nash equilibrium point is discussed through bifurcation diagram, maximum Lyapunov exponent, evolutionary trajectory, and time series diagram. The influence of price adjustment speed on equilibrium price is analyzed. The numerical simulation of price adjustment speed is carried out, which is compared with the actual situation of imported soybean price before and after the trade friction. The results show that the model constructed in this paper can reflect the changing trend of price and demand and predict the short‐term import soybean prices of Brazil and the United States. The forecast accuracy of price fluctuation is high. The results provide model and theoretical reference for price game under trade disputes and provide methodological reference for forecasting the price of imported goods.

Bullwhip effect and complexity analysis in a multi-channel supply chain considering price game with discount sensitivity

This paper constructs a multi-channel supply chain that includes a manufacturer, a dual-channel retailer and an online retailer. The dual-channel retailer has a traditional channel and an online channel, while the manufacturer cooperates with the retailers and opens a direct channel simultaneously. The horizontal and historical price discount sensitivities are taken into account to establish the price-sensitive demand functions. A price game model with the heterogeneous expectations is proposed and analysed with the methods of the stability domain, the bifurcation diagram and the maximum Lyapunov exponent. The complexity and bullwhip effect of each channel are investigated with respect to the price adjustment speed and historical price discount sensitivity. The results show that a moderate or low price discount sensitivity keeps the system stable and a high price discount sensitivity brings the system into the twofold cycle state or chaotic state. It is interesting that if both online channels increase the adjustment speeds with similar strategy the system will enter chaos through the Neimark–Sacker bifurcation. The bullwhip effect is affected by the price adjustment speed and the price discount sensitivity, especially in the double-period or chaotic state, where the bullwhip of the overall supply chain is increased significantly. The results show that controlling price discount sensitivity is useful for supply chain node companies.

The Complexity Analysis for Price Game Model of Risk-Averse Supply Chain Considering Fairness Concern

This paper, considering risk aversion and fair concern, establishes a dynamic price game model of a dual-channel supply chain in which dual-channel retailer sells products through traditional channel and online channel and the online retailer only sells products through online channel. The stability of the system and the influences of different parameter values on utilities are analyzed emphatically using game theory and nonlinear dynamic theory, such as 2D and 3D bifurcation diagram, parameter plot basin, chaos attractor, and sensitivity to initial value. The results find that the system is more likely to lose stability and fall into chaos with the customer demand fluctuating greatly. The system enters into chaos through flip bifurcation with the increase of the price adjustment speed; adjusting the risk-aversion levels or the fairness concern levels of the two retailers can make the system be in a stable state or delay the occurrence of system instability. When the system is in chaos, the average utility of the online retailer will decrease and one of the dual-channel retailers will increase. Using the state feedback control method, the system can return to a stable state from chaos by selecting appropriate control parameters. The research of this paper is of great significance to the decision-makers’ price decision and supply chain operation management.

Construction and Development Strategy of Third Party Cold Chain Logistics System in Jilin Province Based on Financial Risk

This paper analyzes the development status of the industry of third-party cold chain logistics enterprises in Jilin Province, the status of third-party cold chain core enterprises and the relationship of cold chain from a macro perspective, and constructs a scientific evaluation index system to evaluate the third-party cold chain in Jilin Province. The performance of the company analyzes the differences between different enterprise performances, thus guiding the healthy development of third-party cold chain logistics in Jilin Province. At the same time, it constructs the index system of third-party cold chain logistics and financial risk system based on economics theory, analyzes the risk factors of third-party cold chain logistics, further applies scientific methods such as factor analysis to identify key influencing factors, and builds third-party cold chain logistics. Risk early warning indicator system, establish a third-party cold chain logistics risk prevention mechanism. Finally, using regional theory and urban economic basic theory to analyze the urban cold chain logistics distribution system involving third-party cold chain logistics, and the business characteristics, main distribution modes and existing problems of B2B cold chain logistics distribution business and B2C cold chain logistics distribution business [1]. To construct a common distribution demand for the two, the urban cold chain 2B/2C fusion co-distribution model is targeted. Based on the urban cold chain 2B/2C fusion co-distribution model, the pricing game process of third-party cold chain logistics enterprises and fresh e-commerce in the urban cold chain 2B/2C fusion co-distribution model is analyzed, and the B2B cold chain is considered comprehensively by using the game idea. The logistics carries the capacity limitation, establishes the secondary supply chain pricing game model of non-cooperative and cooperative game under different strategies, and builds a third-party cold chain logistics system in Jilin Province, which promotes the cold chain logistics industry in the region to promote the sales of local agricultural products and promote Local economic development.

Pricing Research for a Dual-channel Supply Chain with Free Riding Behavior

As the science and technology are leaping forward, online channels progressively gain the favor of customers based on their unique shopping experience that differs from the traditional retail channels, and establish a dual-channel retail model with the traditional retail channels. The differences between channels will enable consumers to first experience products or services offline, and then buy products online at a cheaper price. This has formed a free-riding effect. Under such effect in dual channels, how e-commerce retailers and traditional retailers determine the price of channel products is to be discussed in this paper. Based on a brief exposition of the current economic environment, the research status of dual-channel and free-rider vehicles is first analyzed to locate the research work of this paper. Then, under this circumstance, the situation is addressed that e-commerce retailers have zero service levels, and the traditional retailer can provide services and establish a pricing game model, the product's dual-channel pricing strategy is analyzed by using the game model. Finally, the actual availability and effectiveness of the built game model are verified with the example analysis.

Research on horizontal integrating strategy pricing game of competitive ports

The homogenization of port services makes the competition among ports fierce. The long construction cycle makes it difficult for port companies to launch new differentiated services. Adopting horizontal integrating strategy to form a regional port group could more or less avoid the over competition for ports. In order to study the change of port companies’ profit, market share from adopting horizontal integrating strategy, this paper developed a multi-objective optimization pricing game model for port companies based on game theory and MNL discrete choosing model and solved the pure strategy nash equilibrium with an numerical algorithm. From the numerical example, we obtained the optimized pricing strategies, integrating routes for highway transportation service as well as sensitivity analysis of user preference factor in the context of horizontal integrating strategy. The result shows that: When user preference factor is 0.008, adopting horizontal integrating strategy could bring 103% profit promotion for port company A and 45% for port company B. While such measure would reduce the profit from adopting vertical integrating strategy. Therefore port companies decide to cancel some integrating routes in both ends of the network in order to reduce the costs. Moreover, there’s a collusion between two companies after adopting horizontal strategy. Decision making of both companies will aim at maximizing the profit of the group. Finally, the sensitivity analysis shows that with the growing of user preference factor θ, profit of regional port group will become stable after a decrease while the difference of profit between two companies become larger. It’s suggested that the regional port group should redistributes the profit so that the cooperation could be more persistent. Finally, port companies should also pay attention to self-development to avoid the profit loss when cooperation breaks or competition from outside.

Product pricing considering the consumer preference based on Internet of Things

With the rapid development of information technology, Internet of things is rapidly penetrated into the manufacturing industry, some manufacturers began to adopt the Internet of things technology to produce intelligent products. Focusing on the pricing of products in the home market under the Internet of things technology environment, the network effect and technological innovation are introduced in the condition that consumers’ preferences are evenly distributed and a pricing game model which can reflect the relationship among manufacturers are constructed. On this basis, the optimal subsidy rate of government is designed based on the principle of social welfare maximization. The results show that, with the advantage of low price of ordinary products, the manufacturer 1 (the ordinary household product manufacturer) can also obtain the corresponding market share. The network effect and the degree of product innovation are the important influencing factors for the manufacturer 2 (the intelligent household product manufacturer) to gain the competitive advantage. Increasing the subsidy rate can effectively stimulate the manufacturer 2 to carry out technological innovation, but it will lead to the decline of the total social welfare level.

Optimization design and computer simulation of enterprise R&D decision model under resource allocation

Taking into account enterprises’ investment on commodity quality and advertisements as important factors that affect sales volume, and the R&D activities are effective measures to reduce production costs and improve commodity competitiveness. Based on the game theory, this paper establishes the price game model among enterprises, and analyzes the relationship of relevant parameters under different competition modes by using computer simulation technology. The simulation results show that the two enterprises will obtain relatively high sales volume and profits in the Stackelberg competition mode, but the absorptive capacity makes the coordination strategy of the R&D stage become unstable. The non-coordination strategy can not only effectively stimulate enterprises to expand the scale of R&D investment to further reduce the cost of production, but also has a positive effect on the follower enterprises in improving sales volume and profits.

Coordinated Pricing Analysis with the Carbon Tax Scheme in a Supply Chain*

ABSTRACTThe carbon tax is a cost‐efficient scheme to curb emissions, and it has been implemented in Australia, British Columbia, and other places worldwide. We aim to analyze its effect on dynamic pricing in a supply chain with multiple suppliers and one manufacturer. The profit‐maximizing manufacturer makes final products using raw materials from suppliers with heterogeneous prices and emission rates. A two‐stage game model is built over an infinite time horizon for this issue. In the first stage, suppliers face price‐dependent demand to set their prices and production rates under the constraint of inventory capacity. Then, in response to the carbon tax scheme, the manufacturer evaluates the procurement prices and emission rates of suppliers to control its emission volumes and sets the sales price of its product. This article predominately focuses on the optimal pricing strategies in a decentralized supply chain. The open‐loop equilibrium and Markovian Nash equilibrium for the dynamic pricing game models of both suppliers and the manufacturer are derived, respectively. The equilibrium prices of suppliers and the manufacturer can be solved based on both irreversible actions and real‐time states. These two types of equilibria can be regarded as the solutions of two different models in specific situations. To analyze the effect of sourcing diversity on pricing strategies and emissions control for the manufacturer, the more general equilibrium price for the manufacturer in an n‐suppliers oligopoly is studied. Numerical examples are presented to illustrate the equilibrium and its monotonicity with various parameter settings.

Pricing policies for complementary products in a dual-channel supply chain

• Four pricing models of complementary products in a dual-channel supply chain are established. • Different market power structures among two manufacturers and the retailer are considered. • Through theoretical and numerical analysis, some managerial insights are obtained. This paper investigates the pricing problem of complementary products in a supply chain with two manufacturers and one retailer, one of the two manufacturers uses dual channels including an online channel and a traditional retail channel to sell its product. We formulate four pricing game models through considering different market power structures of channel members, and derive the corresponding optimal pricing strategies. Based on the theoretical and numerical analysis, we study the effects of consumer channel loyalty, the level of complementarity, and the market power structures on the pricing strategies and the maximal profits of two complementary products. Some interesting and valuable managerial insights are obtained.

Computation of the Stability and Complexity about Triopoly Price Game Model with Delay Decision

We develop the price game model based on the entropy theory and chaos theory, considering the three enterprises are bounded rationality and using the cost function under the resource constraints; that is, the yield increase will bring increased costs. The enterprises of new model adopt the delay decision with the delay parameters τ1 and τ2, respectively. According to the change of delay parameters τ1 and τ2, the bifurcation, stability, and chaos of the system are discussed, and the change of entropy when the system is far away from equilibrium is considered. Prices and profits are found to lose stability and the evolution of the system tends to the equilibrium state of maximum entropy. And it has a big fluctuation with the increase of τ1 and τ2. In the end, the chaos is controlled effectively. The entropy of the system decreases, and the interior reverts to order. The results of this study are of great significance for avoiding the chaos when the enterprises make price decisions.

Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service

Apart from the price fluctuation, the retailers’ service level becomes another key factor that affects the market demand. This paper depicts a modified price and demand game model based on the stochastic demand and the retailer’s service level which influences the market demand decided by customers’ preference, while the market demand is stochastic in this model. We explore how the price adjustment speed affects the stability of the supply chain system with respect to service level and stochastic demand. The dynamic behavior of the system is researched by simulation and the stability domain and the bifurcation phenomenon are shown clearly. The largest Lyapunov exponent and the chaotic attractor are also given to confirm the chaotic characteristic of the system. The simulation results indicate that relatively small price adjustment speed may maintain the system at stable state. With the price adjustment speed gradually increasing, the price system gets unstable and finally becomes chaotic. This chaotic phenomenon will perturb the product market and this phenomenon should be controlled to keep the system stay in the stable region. So the chaos control is done and the chaos can be controlled completely. The conclusion makes significant contribution to the system referring to the price fluctuation based on the service level and stochastic demand.

Price Game Model of Electronic Commerce Retailers and Traditional Retailers with Multi Factor Guidance

Price Game Model of Electronic Commerce Retailers and Traditional Retailers with Multi Factor Guidance

A direct sale model for fresh vegetables based on a dual channel price game model in China

China is the largest vegetable producer in the world. Since 2011, the domestic production and value of vegetables has exceeded food crops, making vegetables the largest agricultural product in China. How to facilitate the efficient distribution of fresh vegetables is concerning more and more people both at home and abroad. Efficient distribution is necessary to balance supply and demand, maintain freshness and to increase farmers' income. In this paper, consumer choice theory provides the theoretical foundation to discuss the necessity and feasibility of a direct sales model. As a relationship exists between distribution channels and consumer preferences in the vegetable market we use convenience as a proxy indicator to build a dual-channel market demand function. We then construct a price game model for a dual-channel market and analyze the results. Finally, we draw our conclusions: (1) the price of the direct sales channel is usually higher than the regular sales channel with the same marginal cost; (2) setting up a direct sales channel will increase producers' profits while reducing the profit of conventional market intermediaries; (3) producers are more likely to change the traditional single channel for direct sales co-existing with traditional channels to reduce costs via e-commerce technology; and (4) the direct sales channel not only expands the conventional channels, but also threatens conventional channel market intermediaries who will make changes or even lower prices in the process of game.

Inbound container storage pricing schemes

In ocean transportation, contractual and operational relationships may be asynchronous. A case in point is the relationship between a customer requiring inbound container storage and a container terminal operator. The customer may store inbound containers in a container terminal and will pay the ocean carrier a specific storage fee, without establishing any contractual relationship with the terminal operator. After collecting the storage fee, the ocean carrier will then pay the container terminal operator for the storage of the inbound container. In this article, we study two-level inbound container storage pricing problems involving a container terminal operator and an ocean carrier in two different inbound container storage contract systems: the free-time contract system and the free-space contract system. In each contract system, we propose a two-stage pricing game model. We derive the optimal decisions for the container terminal operator and the ocean carrier. Analysis about the coordination of the two kinds of contract system is also provided. Numerical studies are conducted to compare the outcomes of the two systems for the ocean carrier and the container terminal. The results of computational experiments reveal that the free-space contract system is a preferable strategy for busy container terminals in terms of traffic control.

Research on the Complex Dynamic Characteristics and RLS Estimation’s Influence Based on Price and Service Game

Considering that the real competitions in service market contain two important factors, price and service, we build a dynamical price and service game model and study the complex dynamics of this bivariate game. Some special properties about the adjustment of service are noted by comparing our innovative bivariate game model with previous univariate game model. Besides, we discuss the stabilities of fixed points and compare the price and service game with price game. What is more, the recursive least-squares (RLS) estimation is introduced to substitute naive estimation; then the impacts of RLS estimation are studied by comparing it with naive estimation.

A Three-Stage Stochastic Dynamic Pricing Game Model Affected by New Products into the Market

In real-life marketing, a common phenomenon is that the prices of current product will have been cut down even the new product has not gone into market yet. Thus, it is very important for merchant to set the strategy which can make the excepted revenue maximum. So, this paper constructs a three-stage stochastic dynamic pricing game model for analyzing the influence of the uncertainty of entry timing of the new products on pricing of products being sold. By analyzing of the pricing strategy, there are big differences in the predictions of new product going into market between merchant and customers; the merchant will adopt cutting price for promotion strategy to reduce negative influence of the new products on the demand of the products sold now. Otherwise, the merchant will adopt the strategy of maximizing current period’s profit.

Lean Cost Management Analysis on Food Processing Enterprise

The aim of this study is to introduce Lean Cost Management (LCM) that tries to create creating value for customers and performs whole cost management in enterprise's entire life cycle under structure of target cost, cost sustaining and cost improvement guided by reverse thinking into food processing enterprise to construct LCM system from aspects of external value chain analysis as well as internal cost management. Dynamic pricing game model was used to provide cost improvement on food enterprise value chain so as to minimize whole cost. The target cost was divided into each part in design phase supported by cost programming, cost reduction and cost improving. Case study shows that such cost suppressing method can reduce cost of food processing enterprises and improve long-term competitiveness.

The User Requirement Based Competitive Price Model for Spectrum Sharing in Cognitive Radio Networks

We analyze the competitive price game model for spectrum sharing in cognitive radio networks with multiple primary users and secondary users and propose a user requirement based competitive price game model for the calculation of the shared spectrum size of cognitive user in Bertrand game. The communication requirement of the cognitive user is quantified into different requirement levels. With the application of spectrum requirement factor, cognitive user can adjust the demanded shared spectrum size according to self-requirement level and the shared spectrum price provided by licensed users. It can avoid the waste of spectrum resource caused by the overdistribution of spectrum to the cognitive user with low communication requirement. Simulation results show that the occupied spectrum of cognitive user can be adjusted with the variation of requirement levels, and the licensed users can achieve better profit performance with consideration of requirement of cognitive user by adjustment of the shared spectrum price proposed spectrum sharing model.