Stackelberg Game Research Articles

Overvoltage risk regulation strategy with distributed energy application in a distribution network based on the Stackelberg game

Along with the increasing low-carbon demand of the power system, the access of a high percentage of renewable energy resources to the distribution network has a large impact on the voltage fluctuation of the system and reduces the operational reliability. In this paper, we consider utilizing the reactive capacity of distributed resources to participate in system voltage regulation to reduce node loss of load probability (LOLP) caused by node overvoltage faults and propose an overvoltage risk regulation strategy for the interaction between distribution network operators (DSOs) and distributed users in the framework of the Stackelberg game. First, the nodes are clustered and analyzed based on the two-dimensional indexes of node voltage regulation ability, and different voltage regulation compensation tariffs are assigned. Second, the cost-benefit model of voltage regulation for the leader and follower sides and the node LOLP model are constructed to measure the reliability of the system. The Stackelberg game is used to co-optimize the two parties’ compensation tariffs and voltage regulation strategies. The optimal solution of voltage regulation under the equilibrium of the game is obtained by solving using the particle swarm optimization (PSO) algorithm. Based on the IEEE-33 node system, a case study is carried out to verify that the proposed overvoltage risk regulation strategy can maximize the benefits of the regulator participants while enhancing the operational reliability of the system.

AoI-Guaranteed Incentive Mechanism for Mobile Crowdsensing With Freshness Concerns

With the explosive spread of smart mobile devices, Mobile CrowdSensing (MCS) has been becoming a promising paradigm, by which a platform can coordinate a group of workers to complete large-scale data collection tasks using their mobile devices. In this paper, we investigate the incentive mechanism design in MCS systems, taking the freshness of collected data and social benefits into consideration. First, the Age of Information (AoI) metric is introduced to measure the freshness of data. Then, we model the incentive mechanism design with AoI guarantees as an incomplete information two-stage Stackelberg game with multiple constraints. Next, we consider the scenario that all participants share the public utility function parameters of the Stackelberg game. By deriving the optimal remuneration paid by the platform and the optimal data update frequency for each worker, and proving the existence of a unique Stackelberg equilibrium, we propose an AoI-guaranteed Incentive Mechanism (AIM) that enables the platform and all workers to maximize their utilities simultaneously. Furthermore, we extend AIM to a general scenario where each participant has no prior knowledge of the utility function parameters of the game. By resorting to the Deep Reinforcement Learning (DRL) technique and modeling the two-stage Stackelberg game as a Markov decision process, we propose a DRL-based Incentive Mechanism (DIM) with AoI guarantees, which makes each participant effectively seek its optimal strategy through trial and error. Meanwhile, the system can guarantee that the AoI values of all data uploaded to the platform are not larger than a given threshold. Finally, numerical experiments on real-world traces are conducted to validate the efficacy and efficiency of AIM and DIM.

Implications of unobservable promotion on distribution channel strategies in a retail platform

Besides distribution services, retail platforms are beginning to provide unobservable promotion services to enhance traffic and demand. Thus, suppliers are incentive to consider the impact of platform promotion on distribution channel strategies. Hence, considering a retail platform supply chain in which the supplier uses an outcome-based contract to incentivize the retail platform’s hidden promotion effort, this paper investigates the implications of unobservable platform promotion on the supplier’s distribution channel strategies. We develop a Stackelberg game model to examine the equilibrium outcomes of reselling and agency selling under unobservable promotion action and find that the retail platform may volunteer to promote in both channels when the market potential difference is large. Interestingly, voluntary promotion may motivate the supplier to increase the wholesale price. Furthermore, we derive conditions under which the supplier prefers reselling and agency selling. When the market potential difference is small, the distribution channel strategy is a threshold policy of the commission rate, below which agency selling is preferred, and reselling is preferred otherwise. It is counterintuitive that when the market potential difference is large, the commission rate will not influence the preference of channel selection and the reselling channel is always preferred by the supplier. Interestingly, the impact of platform promotion on the threshold of distribution channel strategies is non-monotonic in the increment probability of high market potential and market potential difference. Specifically, platform promotion induces the upstream supplier to select the reselling channel suppose the increment probability of high market potential is moderate, while induces the supplier to select the agency selling (reselling) channel when the market potential difference is moderate (large) suppose the increment probability of high market potential is high. Moreover, we find that enhancing the increment probability of high market potential benefits the supplier more, but only moderate increment probability of high market potential makes the retail platform better off.

An optimal “Trade-Online-Deliver-Offline” strategy for recycling unwanted medicines by reutilizing the existent informative pharmaceutical sales network

Circular economy and sustainable development resort to creating friendly and profitable environment of recycling unwanted goods in practice. This research aims to design a novel “Trade-Online-Deliver-Offline” (TODO) system to recycle unwanted medicines (UMs) by reutilizing the existent informative pharmaceutical sales network, which is the first dual-channel recycle system with synergies of manufacturer, chain drugstores and governments. Cross-selling effect, i.e., the additional sales from the customers who visit the drugstores for returning UMs, is also considered in this system. With a given revenue-sharing contract, a bi-level programming model is built to formulate such a recycle system, where the drugmaker is the leader and the chain drugstores are the followers within a decision mode of the Stackelberg game. Through reformulating, this complicated model is solved by developing an efficient smoothing algorithm. Scenario analysis and sensitivity analysis are employed to validate the built model and reveal valuable managerial insights. Main findings include: Compared with the existing modes, the proposed TODO mode is more efficient in terms of the recycled UM quantity and the reduced government burden; Cross-selling effects enhance the profit of drugstores without damage of customer’s surplus, but without significant impacts on the drugmaker’s profit; An increasing revenue-sharing ratio is beneficial to the drugstores in certain scenarios, but reduces the total profit of the recycle system; Resale prices of UMs and governmental tax relief policies both dominate the drugmaker’s optimal ratio of the resold and donated UMs.

An Adaptive Dual-Mode Task-Oriented Resource Management Strategy for GEO Relay Systems

With the fierce global competition on satellite networks, the building of satellite constellations grows explosively. Sharply increasing on-orbit data will face the challenge of satellite-ground data transmission. GEO satellites become the top choice for satellite data relay due to their stable satellite-ground link. Most existing spectrum resource management for GEO relays is equipment-oriented and benefit priority, which may lead to a waste of spectrum resources. In this paper, we propose a real-time task-oriented resource allocation strategy for GEO relay systems. We model the spectrum allocation problem as a distributed non-cooperative Stackelberg game process. We prove that when both sides of the game pursue the maximization of personal revenue, the system will enter a Nash equilibrium state, whereas spectrum resources are not fully used. Based on the maximization of individual utilities (U-prior) and spectrum utilization (S-prior) methods, we design an adaptive dual-mode pricing mode to maximize the spectrum resources within a certain loss of revenue. The simulation results show that the S-prior and U-prior have better performance than the baseline method and existing optimization methods. Our proposed dual-mode strategy is making more throughputs and has less delay with little loss of utility values than that of individual utility maximization.

Navigating the recycling intention of electronics manufacturers in collaborating with a third-party collector: a Stackelberg game analysis

Navigating the recycling intention of electronics manufacturers in collaborating with a third-party collector: a Stackelberg game analysis

Resource Allocation and Pricing in Energy Harvesting Serverless Computing Internet of Things Networks

This paper considers a resource allocation problem involving servers and mobile users (MUs) operating in a serverless edge computing (SEC)-enabled Internet of Things (IoT) network. Each MU has a fixed budget, and each server is powered by the grid and has energy harvesting (EH) capability. Our objective is to maximize the revenue of the operator that operates the said servers and the number of resources purchased by the MUs. We propose a Stackelberg game approach, where servers and MUs act as leaders and followers, respectively. We prove the existence of a Stackelberg game equilibrium and develop an iterative algorithm to determine the final game equilibrium price. Simulation results show that the proposed scheme is efficient in terms of the SEC’s profit and MU’s demand. Moreover, both MUs and SECs gain benefits from renewable energy.

EXPRESS: Who Benefits from Supplier Encroachment in the Presence of Manufacturing Cost Learning?

Manufacturing cost plays a crucial role in suppliers’ encroachment decisions. A high manufacturing cost impedes suppliers’ capacity to encroach. However, cost learning may reduce this cost sufficiently enough to make encroachment profitable for the supplier at a later point in time. Accordingly, he may have an incentive to boost production so as to promote cost learning. Thus, he may drop the wholesale price to induce the retailer to buy more. On the one hand, cost learning may enable encroachment, which may be detrimental to the retailer. On the other hand, cost learning results in a lower manufacturing cost which may translate into a lower future wholesale price, benefiting the retailer. Therefore, the retailer faces a dilemma: should she increase her order quantity to advance cost learning or not? As the retailer may order fewer units in the initial period to limit future direct channel sales, the supplier faces a challenge: should he, instead of dropping his initial wholesale price, raise it to signal his intention of not encroaching so as to induce the retailer to sell a higher quantity in the first period? We model the supplier-retailer interaction as a two-period Stackelberg game to address the retailer’s dilemma and to identify the optimal supplier response. We uncover a new outcome, which arises in the presence of cost learning, where the supplier encroaches but decides not to sell anything through the direct channel. In addition, we find that supplier encroachment may reduce or eliminate the retailer’s incentive to advance cost learning. This results in lower sales by the retailer, which impedes cost learning, leading to a higher future manufacturing cost (compared to the no encroachment setting). As a result, encroachment, which is typically viewed as advantageous for the supplier, may become detrimental to him. Surprisingly, the supplier continues to encroach and sell directly unless he can credibly assure the retailer that he will not encroach in the future.

The complexity analysis of decision-making for horizontal fresh supply chains under a trade-off between fresh-keeping and carbon emission reduction

This study primarily focuses on the impact of carbon emissions generated during the fresh product fresh-keeping process on the traditional fresh supply chain (FSC1) and the low-carbon fresh supply chain with emission reduction behavior (FSC2). Its objective is to investigate how these supply chains dynamically adjust the production quantity, fresh-keeping level, and emission reduction level of fresh products when constrained by the dual-carbon policy. The decision competition model between the two supply chains was explored under two scenarios: the horizontal Nash (HN) game and the long-term Stackelberg (LS) game, wherein FSC1 assumes the role of the leader. The findings indicate that as the carbon tax and carbon trading price increase, the fresh supply chain tends to decrease fresh-keeping intensity while increasing investment in emission reduction. Carbon emissions generated during the fresh product fresh-keeping process have a smaller impact on FSC2's profit than on FSC1, and FSC2 exhibits stronger adaptability under the dual-carbon policy. Irrespective of the game structure, if the adjustment speed of FSC1's production decision exceeds the stable range, its own profit will decrease while the other party's profit will increase. However, if the adjustment speed of FSC2's production decision surpasses the stable range, it will lead to a decrease in profits for both sides. Interestingly, in the LS game, when the adjustment speed of FSC1's production decision exceeds the stable range, FSC1 demonstrates a leader advantage and experiences a rapid increase in profit as the adjustment speed of FSC2's production decision increases, this phenomenon suggests that in the LS game, the leader prevails amidst market chaos.

Blockchain technology for supply chain traceability: A game-theoretic analysis between e-platforms.

In view of the rapid development and application of blockchain technology, this paper considers a secondary supply chain system consisting of a single upstream supplier and a downstream e-tailer that implements blockchain technology and a traditional e-tailer that does not implement blockchain technology. We establish the demand function of two channels based on consumers' sensitivity to the blockchain and use the Stackelberg game model to compare and analyse the e-tailers' profits from the two channels. For the basic properties, interestingly, we find that there exists a critical threshold on the cost sensitivity to effort that helps each e-tailer decide whether to implement effort. If the cost sensitivity to effort is high, the two-sided e-tailers will reduce their effort as much as possible to obtain greater profits. Conversely, if the cost sensitivity to effort is low, they will increase their effort to obtain more benefits. We also discuss the role of blockchain technology in competition between e-tailers and analyse the impact of the product brand effect brought by the traceability characteristic of blockchain on the competition between e-tailers. To check the robustness of the core results and to investigate different forms of supply chain configurations, this paper further develops the analysis of the supplier entering agency agreements with two-sided e-tailers. Under this scenario, the supplier sells their products directly to consumers through two-sided e-platforms and shares revenue with e-tailers as platform agency fees. These core ideas remain valid in the extended model.

Mean-Field Stackelberg Game-Based Security Defense and Resource Optimization in Edge Computing

Edge computing brings computation and storage resources to the edge of the mobile network to solve the problems of low latency and high real-time demand. However, edge computing is more vulnerable to malicious attacks due to its open and dynamic environments. In this article, we investigate security defense strategies in edge computing systems, focusing on scenarios with one attacker and multiple defenders to determine optimal defense strategies with minimal resource allocation. Firstly, we formulate the interactions between the defenders and the attackers as the mean-field Stackelberg game model, where the state and the objective functions of the defenders are coupled through the mean-field term, and are strongly influenced by the strategy of the attacker. Then, we analyze the local optimal strategies of the defenders given an arbitrary strategy of the attackers. We demonstrate the Nash equilibrium and the mean-field equilibrium for both the defenders and the attackers. Finally, simulation analysis will illustrate the dynamic evolution of the defense strategy of the defenders and the trajectory of the attackers based on the proposed Stackelberg game model.

For-profit or for-CSR: decisions of power batteries recovery in the supply chain

Abstract The importance of recovering retired batteries from new energy vehicles (NEVs) has garnered widespread attention in both scholarly literature and practical applications. This paper discusses the decisions of battery recovery in a supply chain consisting of a supplier and a manufacturer. Utilizing the Stackelberg game, we construct the models and compare the equilibrium solutions in two decision-making modes, for-profit and for-CSR (corporate social responsibility). The conclusion shows that the firms’ pursuit of CSR contributes to increasing collection prices. However, if environmental damage is severe, the firms’ pursuit of CSR leads to high retail prices, which is detrimental to the sale of NEVs. Furthermore, although not all members’ collection amounts increase when considering CSR, the overall collection effect will be better. Meanwhile, we find that both the supplier and the manufacturer have incentives to practise CSR because their pursuit of CSR leads to high profits. Finally, this paper has verified all the above conclusions using theoretical data.

Research on Channel Encroachment Strategy and Contract Design of Manufacturers Based on Live Broadcast

This article constructs supply chain models after the manufacturer's live streaming channel encroachment. Through demand function models and Stackelberg game theory, the optimal decisions of each member in the supply chain are solved using reverse induction method. The impact of various parameters on invasion strategies such as quality investment, channel pricing, and profits of all parties is analyzed. The results indicate that when consumers have a high level of preference for the sales channels opened by manufacturers, manufacturers can gain higher profits by inviting internet celebrities to live stream and promote sales through channel encroachment. When the potential demand scale of manufacturers is low and the proportion of anchor sharing is higher, manufacturers should reduce quality costs by lowering the level of quality investment. When the potential demand scale of manufacturers is high, they should reduce product returns by increasing the quality investment level and incentivize broadcasters by raising live broadcast prices.

Design of distributed trading mechanism for prosumers considering the psychological gap effect in community electricity markets

With the large-scale customer-side development of distributed energy and continuous advancements in power market reform, the market-oriented trading of distributed power generation with the participation of prosumers has gradually become an important solution to promote the consumption of distributed energy. In addition, prosumers exhibit obvious bounded rationality characteristics; therefore, the design of efficient and reasonable trading mechanisms determines the efficiency of the market. From this perspective, a distributed electricity market trading mechanism based on the Stackelberg game is proposed for the community electricity trading market, with multiple prosumers participating in the distribution side. Firstly, the trading architecture of the community electricity market was established under the distribution network level. Secondly, the pricing strategy of the distribution network operator and the quantitative strategy of community prosumers were analysed; on this basis, the characteristics of the bounded rationality of prosumers were considered, and the impact of the psychological gap effect of prosumers on their energy utility was introduced into the objective function of prosumers. This facilitated the construction of a Stackelberg game model in which distribution network operators lead and community prosumers follow. Thirdly, the Stackelberg equilibrium was proven to exist and be unique, which was then solved by the distributed algorithm – combining the evolutionary algorithm and quadratic programming – which improves the solution efficiency and effectively protects the privacy of prosumers. Finally, the effectiveness and feasibility of the proposed trading mechanism were verified through numerical examples.

Linear-quadratic two-person differential game: Nash game versus Stackelberg game, local information versus global information

Linear-quadratic two-person differential game: Nash game versus Stackelberg game, local information versus global information

Decentralized multi-agent reinforcement learning based on best-response policies.

Introduction: Multi-agent systems are an interdisciplinary research field that describes the concept of multiple decisive individuals interacting with a usually partially observable environment. Given the recent advances in single-agent reinforcement learning, multi-agent reinforcement learning (RL) has gained tremendous interest in recent years. Most research studies apply a fully centralized learning scheme to ease the transfer from the single-agent domain to multi-agent systems. Methods: In contrast, we claim that a decentralized learning scheme is preferable for applications in real-world scenarios as this allows deploying a learning algorithm on an individual robot rather than deploying the algorithm to a complete fleet of robots. Therefore, this article outlines a novel actor-critic (AC) approach tailored to cooperative MARL problems in sparsely rewarded domains. Our approach decouples the MARL problem into a set of distributed agents that model the other agents as responsive entities. In particular, we propose using two separate critics per agent to distinguish between the joint task reward and agent-based costs as commonly applied within multi-robot planning. On one hand, the agent-based critic intends to decrease agent-specific costs. On the other hand, each agent intends to optimize the joint team reward based on the joint task critic. As this critic still depends on the joint action of all agents, we outline two suitable behavior models based on Stackelberg games: a game against nature and a dyadic game against each agent. Following these behavior models, our algorithm allows fully decentralized execution and training. Results and Discussion: We evaluate our presented method using the proposed behavior models within a sparsely rewarded simulated multi-agent environment. Although our approach already outperforms the state-of-the-art learners, we conclude this article by outlining possible extensions of our algorithm that future research may build upon.

Construction and Application of the Double Game Model for Direct Purchase of Electricity by Large Consumers under Consideration of Risk Factors

With the development of global clean energy and the implementation of carbon emission reduction policies, the direct purchase of electricity by large consumers has been increasingly promoted as a special form of electricity trading. Therefore, on the basis of the completion of low-carbon emission reduction targets in each country, how to rationalize the electricity purchase by large consumers in the electricity market so as to reduce their electricity purchase costs has become the main target of attention in each country. Currently, there are fewer studies in existing research on the direct electricity purchase strategy of large consumers under the consideration of the weight of consumption responsibility and risk. Based on this, this paper constructs a dual-game model for direct electricity purchase by large consumers based on the Stackelberg game and non-cooperative game theory. The concept of value at risk is further introduced, and the optimal strategy of direct electricity purchase by large consumers is proposed. The results of this study show that when market players make decisions on the purchase and sale of electricity, power suppliers will increase their biddings to obtain the highest returns, and large consumers can reduce the transaction costs by combining the medium- and long-term market with the spot market to purchase electricity. In the choice of electricity purchase market, with the increasing risk factor, large consumers shift from the risky spot market to the less risky medium- and long-term market and option market. This paper provides a reference for the issues of power suppliers’ contract bidding and large consumers’ electricity purchase strategy in the medium- and long-term contract transactions.

Optimal decisions of retailer's loans from bank

AbstractThis study employs the Stackelberg game model to explore an innovative financing model where the retailer directly borrows from the bank under conditions of symmetric information. Diverging from traditional research, this study uniquely incorporates the concept of the margin rate into the decentralised decision analysis among retailer, supplier, and bank. The finding indicates that the capital of the retailer and margin rate significantly influence financing decisions within the supply chain, thereby impacting profitability for all stakeholders. Specifically, we find that the margin rate plays a crucial role in optimising retailer financing decisions, supplier pricing strategies, and bank risk management. These insights offer a fresh perspective for banks to establish appropriate margin rates and loan interest rates, effectively managing loan risks and maximising supply chain profitability.

Closed-loop Supply Chain Model Analysis of Home Appliances based on Promotional Effort and Recycling Effort

Nowadays, a large number of home appliances have entered the node of renewal, if they can be properly disposed of and utilised, used home appliances can also be converted into renewable resources to achieve the economic cycle, and at the same time, green living and circular economy are increasingly accepted by the public. Recycling of used home appliances has both economic and social benefits. At the same time, promotional efforts invested in the market for home appliances have an obvious effect on increasing their market demand. Therefore, it is necessary to study the closed-loop supply chain of home appliances based on promotion and recycling efforts. In this paper, we use literature analysis, mathematical analysis and Stackelberg game analysis to construct a closed-loop supply chain model for home appliances based on promotional and recycling efforts after determining who is the promoter among manufacturers and retailers, and then compare and analyse the decisions and benefits of the supply chain members, taking into account their centralised and decentralised decision-making. The results of this paper show that: (1) when home appliance manufacturers, retailers and third-party recyclers of used home appliances make decentralised decisions, there is a double marginal effect, i.e., the supply chain members only consider their own benefits while ignoring the benefits of the supply chain as a whole, which results in the failure of this closed-loop supply chain system of home appliances to be coordinated. (2) When the retailer's promotional effort is greater, both the retail price and the retailer's profit are lower. (3) The greater the recycling effort of the third-party recycler of used home appliance products, the higher its recycling price, i.e., the consequent increase in recycling costs, leading to a decrease in its profit.

Optimal Planning of User-side Scaled Distributed Generation Based on Stackelberg Game

BACKGROUND: User-side distributed generation represented by distributed photovoltaic and distributed wind turbine has shown an expansion trend of decentralized construction and disordered access, which is difficult to satisfy the demand for large-scale exploitation and sustainable development of distributed generation under the low-carbon transformation vision of the power system.
 OBJECTIVES: To address the interest conflict and operation security problems caused by scaled distributed generation accessing the distribution network, this paper proposes the optimal planning method of user-side scaled distributed generation based on the Stackelberg game.
 METHODS: Firstly, a cluster planning and operation mode of distributed generation is established. Then, a prediction method for planning behavior of user-side distributed generation is proposed in order to predict whether users will adopt the self-build mode or the leasing site mode for distributed generation. Finally, in order to reveal the game relationship between the distribution network operator and the users in the allocation of distributed generation resources, a bi-level planning model for scaled distributed generation is established based on the Stackelberg game.
 RESULTS: The simulation results show that the revenue of the distribution network operator under the gaming model increases by 10.15% and 16.88% compared to the models of all users self-build distributed generation and all users leasing distributed generation site, respectively, while at the same time, individual users also realize different degrees of revenue increase.
 CONCLUSION: The case analysis validates the effectiveness of the proposed method in guiding the rational and efficient planning of user-side distributed generation.