A Game Model for Medical Service Pricing Based on the Diagnosis Related Groups

Background: Currently there are various issues that exist in the medical institutions in China as a result of the price-setting in DRGs, which include the fact that medical institutions tend to choose patients and that the payment standard for complex cases cannot reasonably compensate the cost.Objective: The main objective is to prevent adverse selection problems in the operations of a diagnosis-related groups (DRGs) system with the game pricing model for scientific and reasonable pricing.Methods: The study proposes an improved bargaining game model over three stages, with the government and patients forming an alliance. The first stage assumes the alliance is the price maker in the Stackelberg game to maximize social welfare. Medical institutions are a price taker and decide the level of quality of medical service to maximize their revenue. A Stackelberg equilibrium solution is obtained. The second stage assumes medical institutions dominate the Stackelberg game and set an optimal service quality for maximizing their revenues. The alliance as the price taker decides the price to maximize the social welfare. Another Stackelberg equilibrium solution is achieved. The final stage establishes a Rubinstein bargaining game model to combine the Stackelberg equilibrium solutions in the first and second stage. A new equilibrium between the alliance and medical institutions is established.Results: The results show that if the price elasticity of demand increases, the ratio of cost compensation on medical institutions will increase, and the equilibrium price will increase. The equilibrium price is associated with the coefficient of patients' quality preference. The absolute risk aversion coefficient of patients affects government compensation and total social welfare.Conclusion: In a DRGs system, considering the demand elasticity and the quality preference of patients, medical service pricing can prevent an adverse selection problem. In the future, we plan to generalize these models to DRGs pricing systems with the effects of competition of medical institutions. In addition, we suggest considering the differential compensation for general hospitals and community hospitals in a DRGs system, in order to promote the goal of hierarchical diagnosis and treatment.

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Assessment of Medical Service Pricing in China's Healthcare System: Challenges, Constraints, and Policy Recommendations

Frontiers in Public Health ◽

10.3389/fpubh.2021.787865 ◽

2021 ◽

Vol 9 ◽

Author(s):

Wenying Xiong ◽

Yufan Deng ◽

Yili Yang ◽

Yumeng Zhang ◽

Jay Pan

Keyword(s):

Healthcare System ◽

Health Reform ◽

Medical Service ◽

Medical Services ◽

Policy Recommendations ◽

Constraint Factors ◽

Medical Institutions ◽

Service Pricing ◽

Multiple Constraint

Medical service pricing reform was considered as one of the focuses of China's remarkable health reform. This paper preliminarily assessed the roles of medical service pricing in the context of China's healthcare system. Specifically, we described the potential roles of medical service pricing in China and pointed out relevant challenges that emerged in practice as the result of reform-related activities. Multiple constraint factors that might have induced undesired outcomes were then recognized, including the excessive diversity and specialization of medical services, the price inelasticity of patients' demand, and the inadequate capability of both medical institutions and administrations. Finally, we provided policy recommendations to inform the ongoing medical service pricing reform in China from a long-term perspective.

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The service pricing strategies and the strategic behavior of customers in an unobservable Markovian queue with unreliable server

RAIRO - Operations Research ◽

10.1051/ro/2021181 ◽

2021 ◽

Author(s):

Kamel Meziani ◽

Fazia RAHMOUNE ◽

Mohammed Said RADJEF

Keyword(s):

Strategic Behavior ◽

Stackelberg Game ◽

Stackelberg Equilibrium ◽

Pricing Strategies ◽

Behavioral Strategies ◽

System Parameters ◽

Service Pricing ◽

Markovian Queue ◽

Proposed Model ◽

The Social

A Stackelberg game is used to study the service pricing and the strategic behavior of customers in an unreliable and totally unobservable M/M/1 queue under a reward-cost structure. At the first stage, the server manager, acting as a leader, chooses a service price and, at the second stage, a customer, arriving at the system and acting as a follower, chooses to join the system or an outside opportunity, knowing only the service price imposed by the server manager and the system parameters. We show that the constructed game admits an equilibrium and we give explicit forms of server manager and customers equilibrium behavioral strategies. The results of the proposed model show that the assumption that customers are risk-neutral is fundamental for the standard approach usually used. Moreover, we determine the socially optimal price that maximizes the social welfare and we compare it to the Stackelberg equilibrium. We illustrate, by numerical examples, the effect of some system parameters on the equilibrium service price and the revenue of the server manager.

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Cloud Provider's Response to Multiple Models of Attack Behaviors

Recent Patents on Engineering ◽

10.2174/1872212112666180918165944 ◽

2019 ◽

Vol 13 (4) ◽

pp. 325-333

Author(s):

Xu Liu ◽

Xiaoqiang Di ◽

Jinqing Li ◽

Huamin Yang ◽

Ligang Cong ◽

...

Keyword(s):

Stackelberg Game ◽

Multiple Models ◽

Theoretic Model ◽

Cloud Provider ◽

Game Model ◽

Attack Behavior ◽

Behavior Model ◽

Protection Strategy ◽

Behavior Models ◽

Optimal Protection

Background: User behavior models have been widely used to simulate attack behaviors in the security domain. We revised all patents related to response to attack behavior models. How to decide the protected target against multiple models of attack behaviors is studied. Methods: We utilize one perfect rational and three bounded rational behavior models to simulate attack behaviors in cloud computing, and then investigate cloud provider’s response based on Stackelberg game. The cloud provider plays the role of defender and it is assumed to be intelligent enough to predict the attack behavior model. Based on the prediction accuracy, two schemes are built in two situations. Results: If the defender can predict the attack behavior model accurately, a single-objective game model is built to find the optimal protection strategy; otherwise, a multi-objective game model is built to find the optimal protection strategy. Conclusion: The numerical results prove that the game theoretic model performs better in the corresponding situation.

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Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand

Sustainability ◽

10.3390/su13158271 ◽

2021 ◽

Vol 13 (15) ◽

pp. 8271

Author(s):

Yaqing Xu ◽

Jiang Zhang ◽

Zihao Chen ◽

Yihua Wei

Keyword(s):

Dynamic Programming ◽

Supply Chain ◽

Computational Complexity ◽

Stackelberg Game ◽

Programming Model ◽

Dynamic Programming Method ◽

Game Model ◽

Chain Model ◽

Stochastic Demands ◽

Demand Models

Although there are highly discrete stochastic demands in practical supply chain problems, they are seldom considered in the research on supply chain systems, especially the single-manufacturer multi-retailer supply chain systems. There are no significant differences between continuous and discrete demand supply chain models, but the solutions for discrete random demand models are more challenging and difficult. This paper studies a supply chain system of a single manufacturer and multiple retailers with discrete stochastic demands. Each retailer faces a random discrete demand, and the manufacturer utilizes different wholesale prices to influence each retailer’s ordering decision. Both Make-To-Order and Make-To-Stock scenarios are considered. For each scenario, the corresponding Stackelberg game model is constructed respectively. By proving a series of theorems, we transfer the solution of the game model into non-linear integer programming model, which can be easily solved by a dynamic programming method. However, with the increase in the number of retailers and the production capacity of manufacturers, the computational complexity of dynamic programming drastically increases due to the Dimension Barrier. Therefore, the Fast Fourier Transform (FFT) approach is introduced, which significantly reduces the computational complexity of solving the supply chain model.

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Pricing Policies in a Retailer Stackelberg O2O Green Supply Chain

Sustainability ◽

10.3390/su12083236 ◽

2020 ◽

Vol 12 (8) ◽

pp. 3236

Author(s):

Gan Wan ◽

Gang Kou ◽

Tie Li ◽

Feng Xiao ◽

Yang Chen

Keyword(s):

Supply Chain ◽

Stackelberg Game ◽

Good Combination ◽

Green Supply Chain ◽

Game Model ◽

Mathematical Function ◽

Pricing Strategies ◽

Direct Channel ◽

Retail Channel ◽

Offline Channels

Due to the popularization of the concept of “new retailing”, we study a new commercial model named O2O (online-to-offline), which is a good combination model of a direct channel and a traditional retail channel. We analyze an O2O supply chain in which manufacturers are responsible for making green products and selling them through both online and offline channels. The retailer is responsible for all online and offline channels’ orders, and the manufacturer gives the retailer a fixed fee. We construct a mathematical function model and analyze the greenness and pricing strategies of centralized and decentralized settings through the retailer Stackelberg game model. Due to the effects of the double marginalization of supply chain members, we adopt a simple contract to coordinate the green supply chain. The paper’s contributions are that we obtain pricing and greening strategies by taking the cooperation of offline channels and online channels into consideration under the O2O green supply chain environment.

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Optimal Decision-Making to Charge Electric Vehicles in Heterogeneous Networks: Stackelberg Game Approach

Energies ◽

10.3390/en12020325 ◽

2019 ◽

Vol 12 (2) ◽

pp. 325 ◽

Cited By ~ 2

Author(s):

Shijun Chen ◽

Huwei Chen ◽

Shanhe Jiang

Keyword(s):

Electric Vehicles ◽

Heterogeneous Networks ◽

Demand Uncertainty ◽

Stackelberg Game ◽

Optimal Solution ◽

Stackelberg Equilibrium ◽

Optimal Decision ◽

Charging Station ◽

Simulation Results ◽

Grid Operators

Electric vehicles (EVs) are designed to improve the efficiency of energy and prevent the environment from being polluted, when they are widely and reasonably used in the transport system. However, due to the feature of EV’s batteries, the charging problem plays an important role in the application of EVs. Fortunately, with the help of advanced technologies, charging stations powered by smart grid operators (SGOs) can easily and conveniently solve the problems and supply charging service to EV users. In this paper, we consider that EVs will be charged by charging station operators (CSOs) in heterogeneous networks (Hetnet), through which they can exchange the information with each other. Considering the trading relationship among EV users, CSOs, and SGOs, we design their own utility functions in Hetnet, where the demand uncertainty is taken into account. In order to maximize the profits, we formulate this charging problem as a four-stage Stackelberg game, through which the optimal strategy is studied and analyzed. In the Stackelberg game model, we theoretically prove and discuss the existence and uniqueness of the Stackelberg equilibrium (SE). Using the proposed iterative algorithm, the optimal solution can be obtained in the optimization problem. The performance of the strategy is shown in the simulation results. It is shown that the simulation results confirm the efficiency of the model in Hetnet.

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Demand Subsidy versus Production Regulation: Development of New Energy Vehicles in a Competitive Environment

Mathematics ◽

10.3390/math9111280 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1280

Author(s):

Zixuan Wang ◽

Xiuzhang Li

Keyword(s):

Social Welfare ◽

Stackelberg Game ◽

Positive Impact ◽

Consumer Preference ◽

Social Planner ◽

Environmental Preferences ◽

The Social ◽

New Energy ◽

Vehicle Market ◽

New Energy Vehicles

In the competitive market environment, the growth of new energy vehicles (NEVs) faces many obstacles. Demand subsidy or production regulation-related policies are widely used to promote the development of NEVs. A comparative analysis of the effects of the two types of policies on the competitive vehicle market requires further study. To fill this gap, we investigate which type of policy is more preferable from the perspective of the social planner. In this paper, we construct a Stackelberg game with a welfare-maximizing social planner and two profit-maximizing manufacturers producing NEVs and fuel vehicles (FVs), respectively. Interestingly, although both types of policies can increase the quantity of NEVs, demand subsidy also promotes the growth of total vehicles at the same time; in contrast, production regulation reduces the total vehicles. Moreover, compared with the benchmark that no policy intervention, demand subsidy generally improves social welfare, while production regulation improves social welfare only with high consumer preference for NEVs. Nevertheless, production regulation always has a positive impact on the environment, whereas demand subsidy may have a positive impact only when the NEV is very environment friendly. The numerical results show that consumer environmental preferences and the regulation of environmental impact determine which type of policy dominates the other.

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Revenue Sharing Contract of Green Supply Chain under Manufacturer Risk-Aversion

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.697.482 ◽

2014 ◽

Vol 697 ◽

pp. 482-487

Author(s):

Shi Ying Jiang ◽

Chun Yan Ma

Keyword(s):

Decision Making ◽

Supply Chain ◽

Risk Aversion ◽

Stackelberg Game ◽

Wholesale Price ◽

Revenue Sharing ◽

Green Supply Chain ◽

Game Model ◽

Product Price ◽

Revenue Sharing Contract

Background on two stages green supply chain consisting of a manufacturer and a retailer, considering the degree of risk aversion and product greenness, consumer preferences and other factors, the centralized decision-making game model and manufacturer-leading Stackelberg game model are established.Then two game models are compared. The interaction of product greenness, wholesale price, product price,and risk aversion utility for manufacturers and retailers are also disscussed. Finally, the revenue sharing contract is applied to coordinate the green supply chain . The results show that:(1) In the centralized decision-making model, there is a critical value of the product green degree; (2)In manufacturer-leading Stackelberg game model, the higher the green degree of the product, the higher the manufacturer's wholesale price,and the wholesale price increases as risk aversion degree of manufacturers improves;(3)The revenue sharing contract can coordinate this type of green supply chain under manufacturers risk-averse.

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Manufacturing service order allocation in the context of social manufacturing based on Stackelberg game

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405418808190 ◽

2018 ◽

Vol 233 (8) ◽

pp. 1890-1901

Author(s):

Wei Guo ◽

Pingyu Jiang

Keyword(s):

Quality Of Service ◽

Nash Equilibrium ◽

Manufacturing Industry ◽

Stackelberg Game ◽

Game Model ◽

Service Cost ◽

Order Allocation ◽

Multi Objective ◽

Bird Swarm Algorithm

For adapting the socialization, individuation and servitization in manufacturing industry, a new manufacturing paradigm called social manufacturing has received a lot of attention. Social manufacturing can be seen as a network that enterprises with socialized resources self-organized into communities that provide personalized machining and service capabilities to customers. Since a community of social manufacturing has multiple enterprises and emphasizes on the importance of service, manufacturing service order allocation must be studied from the new perspective considering objectives on service cost and quality of service. The manufacturing service order allocation can be seen as a one-to-many game model with multi-objective. In this article, a Stackelberg game model is proposed to tackle the manufacturing service order allocation problem with considering the payoffs on cost and quality of service. Since this Stackelberg game can be mapped to a multi-objective bi-level programming, a modified multi-objective hierarchical Bird Swarm Algorithm is used to find the Nash equilibrium of the game. Finally, a case from a professional printing firm is analyzed to validate the proposed methodology and model. The objective of this research is to find the Nash equilibrium on the manufacturing service order allocation and provide strategies guidance for customer and small- and medium-sized enterprises with optimal service cost and lead time. According to the game process and Nash equilibrium, some rules are revealed, and they are useful for guiding practical production.

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Research on Pricing Decision of Direct Sales Green Supply Chain Based on Consumers’ Valuation

Discrete Dynamics in Nature and Society ◽

10.1155/2021/7743647 ◽

2021 ◽

Vol 2021 ◽

pp. 1-17

Author(s):

Yong-Gang Ye ◽

Xiao-Feng Liu

Keyword(s):

Supply Chain ◽

Simulation Analysis ◽

Stackelberg Game ◽

Game Model ◽

Direct Sales ◽

Equilibrium Prices ◽

Theoretical Support ◽

Pricing Decision ◽

Negative Effect ◽

Product Valuation

Consumer’s valuation of merchandise is an important factor affecting consumer buying behavior. When the consumer’s valuation exceeds the price of product, the consumer generally makes a decision to purchase the product; conversely, when the consumer’s estimate is lower than the price of product, the consumer will usually refuse to buy the product. From the perspective of consumer product valuation, this study assumed that the consumer’s product valuation obeys a uniform distribution, and a novel consumer demand function was proposed. On this basis, we studied enterprises’ pricing decisions in the supply chain of green agricultural products and obtained the equilibrium prices and optimal profits of the enterprises in several different scenarios, including Vertical Nash game model (VNM), firm A Stackelberg game model (FASM), firm B Stackelberg game model (FBSM), and cooperative game model (CM). In addition, the influence of parameters, such as green level, green preference payment coefficient, and green cost on the optimal profit, was discussed based on game theory and numerical simulation analysis. It was found that equilibrium prices always existed in several different scenarios, and when consumer’s green preference payment coefficient was large enough, the optimal profit of firm B was greater than the optimal profit of firm A. Furthermore, in CM, the sum of optimal profit of firm A and optimal profit of firm B is maximum for four scenarios. Finally, in the three competitive scenarios, green level, green preference payment coefficient, and green cost, have a positive or negative effect on the optimal profits of firm A or firm B. The research conclusions of this study provided theoretical support for the decision-making of enterprises and related management departments.

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