Equilibrium Strategies Research Articles

A two-layer stochastic game approach to reinsurance contracting and competition

We propose a two-layer stochastic game model to study reinsurance contracting and competition in a market with one insurer and two competing reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional reinsurance contracts that are priced using the variance premium principle. The reinsurance contracting between the insurer and each reinsurer is modeled as a Stackelberg game. The two reinsurers compete for business from the insurer and optimize the so-called relative performance, instead of their own surplus, and their competition is settled by a noncooperative Nash game. We obtain a sufficient and necessary condition, related to the competition degrees of the two reinsurers, for the existence of an equilibrium. We show that the equilibrium, if exists, is unique, and the equilibrium strategy of each player is constant, fully characterized in semiclosed form. Furthermore, we obtain interesting sensitivity results for the equilibrium strategies through both analytical and numerical studies.

Leveraging intergovernmental data sharing for digital transformation in ecological and environmental protection

The data-sharing problem in the digital transformation of ecological environmental protection is a result of complex interactions and continuous strategic interactions among governments. While existing research has focused on the application and impact of digital technologies in ecological environmental protection, there remains a paucity of micro-level investigations into data sharing among different local governments regarding ecological environment protection. Notably, the issue of data barriers between local governments is particularly prominent. This paper analyzes the data-sharing problem in the digital transformation of ecological environmental protection through an evolutionary game model involving central and local governments, providing new perspectives and methods for understanding and improving data sharing and governance of ecological environmental protection, thereby promoting the digital transformation of the ecological environmental governance system and governance capacity. It finds that six stable equilibrium strategies can form based on local government participation levels, with the superior government's active promotion and regulation being crucial for achieving stable, multi-party participation. Key factors include the superior government's administrative costs and incentives, and local governments' benefits, costs, and risk considerations. The study highlights the importance of benefit-sharing rules and provides optimization strategies for enhancing intergovernmental data sharing.

Solving the prisoner’s dilemma trap in Hamilton’s model of temporarily formed random groups

Explaining the evolution of cooperation in the strong altruism scenario, where a cooperator does not benefit from her contribution to the public goods, is a challenging problem that requires positive assortment among cooperators (i.e., cooperators must tend to associate with other cooperators) or punishment of defectors. The need for these drastic measures stems from the analysis of a group selection model of temporarily formed random groups introduced by Hamilton nearly fifty years ago to describe the fate of altruistic behavior in a population. Challenging conventional wisdom, we show analytically here that strong altruism evolves in Hamilton’s original model in the case of biparental sexual reproduction. Moreover, when the cost of cooperation is small and the amplified contribution shared by group members is large, cooperation is the only stable strategy in equilibrium. Thus, our results provide a solution to the ‘problem of origination’ of strong altruism, i.e. how cooperation can take off from an initial low frequency of cooperators. We discuss a possible reassessment of cooperation in cases of viral co-infection, as cooperation may even be favored in situations where the prisoner’s dilemma applies.

Alpha-robust mean–variance reinsurance and investment strategies with transaction costs

This paper investigates the time-consistent reinsurance and investment strategies for insurers based on the alpha-robust mean–variance criterion. We assume that transaction costs with quadratic form exist in the financial market composed of a risk-free asset and n risky assets, and the insurance and financial markets are correlated. By solving a system of extended HJB equations, the equilibrium reinsurance and investment strategy and the corresponding value function are derived in terms of the solution to a system of matrix Riccati equations. In some special cases, more explicit expressions for the equilibrium strategies and value functions are provided. Numerical examples demonstrate that the growth rate of investment slows down as the transaction costs level or the correlation coefficient increases. In addition, we find that the transaction costs level has opposite effects on the utility losses due to ignoring jumps or ambiguity.

Under the context of competition between platform sales and live streaming sales, who has the pricing power of products?

The rapid rise of live-streaming selling and the increasing diversity of e-commerce channels have sparked ongoing debates regarding product pricing power. This price competition behaviour of online dual channels triggered by the supply-side pricing dilemma is a topic of significant research interest and forms the focal point of this paper. Therefore, we leverage the principles of game theory to construct a three-party evolutionary game model consisting of a brand, a steamer, and a traditional e-commerce platform. Within this framework, the brand holds the primary pricing authority. Our analysis examines the equilibrium strategies adopted by the various players under diverse scenarios and explores how the evolving behaviours of these parties impact the overall game system. Additionally, we employ the “people-goods-scene” perspective to deconstruct the intricate dynamics within this complex supply chain ecosystem. Our findings reveal two distinct evolutionary stable strategies: one in which brands maintain a stance against low-price negotiation, streamers avoid bargaining, and platforms avoid providing subsidies; the other in which brands are open to negotiating low prices, streamers engage in bargaining, and platforms provide subsidies. Notably, in most cases, brands tend to avoid explicitly stating their opposition to low-price negotiation. However, if a brand’s strategy shifts towards rejecting such negotiation, the negative implications of price wars across channels become a critical consideration. Conversely, when a brand opts for a more concessive pricing strategy, we need to consider the potential positive impacts of low-price competition.

Tullock contest with reference‐dependent preferences

AbstractWe study the Tullock contest model with loss aversion and endogenously formed reference points. In a contest with n possibly heterogeneous players and convex effort costs, we establish sufficient conditions for a unique Nash equilibrium in pure strategies. Subsequently, we analyze the impact of loss aversion on players' spending behavior, probability of winning, and rent dissipation.

Study on the Selection of Recycling Strategies for the Echelon Utilization of Electric Vehicle Batteries under the Carbon Trading Policy

Global climate change has prompted all sectors of society to take urgent action to reduce carbon emissions. Electric vehicles are the key to low-carbon transportation transformation, but their popularity has led to difficulties in disposing of used batteries. Improper handling will pollute the environment and violate the original goal of promoting low-carbon practices. Therefore, it is crucial to establish a sustainable battery-recycling and disposal system. This study uniquely incorporates the concept of battery echelon utilization into its analytical framework using a Stackelberg game model, exploring the equilibrium strategies for stakeholders in a closed-loop supply chain under carbon emission constraints. We analyzed the impact of multiple factors in the recycling process, as well as the influence of digital technology, on enterprise pricing, recycling efficiency, and the choice of recycling channels. The study found that the market pricing of batteries and electric vehicles is not influenced by recycling participants, but is instead related to the application of digital technology. Numerical simulations further reveal that the battery’s echelon utilization rate and carbon emission limit policies jointly motivate enterprises to be more proactive in recycling. In the joint recycling model, battery suppliers can achieve more substantial profit growth compared to electric vehicle manufacturers, providing new insights and directions for innovation and the development of collaborative models within the supply chain.

Strategic logistics service choices for online platforms: self-operated, third-party or agency logistics?

Self-operated and third-party products in platform retailing can be delivered by self-operated or third-party physical distribution. However, how choosing the best logistics service mode represents a difficult problem for online platforms and sellers in practice. This paper analyzes the strategic logistics service mode choices for retail sales on an online platform. Equilibrium strategies are derived by solving game models considering three logistics service modes: self-operated, third-party and agency. The results show that the platform has an incentive to provide self-operated physical distribution to the seller when the distribution commission exceeds a threshold. More specifically, it achieves a win–win situation with the seller in the self-operated logistics service mode when the distribution commission falls within a moderate range. The platform is unwilling to provide any logistics services with a sufficient low distribution commission. Except in the case of high distribution commission and low self-operated distribution quality, the seller would prefer to accept the platform’s self-operated physical distribution. In addition, the third-party physical distribution company generally prefers the agency logistics service mode unless the self-operated distribution quality and commission are high.

Hybrid financing in a dual‐channel supply chain with asymmetric demand information

AbstractThis study delves into the interaction between hybrid financing and asymmetric demand information within a dual‐channel supply chain. In this setup, the supplier directly sells to customers and also through a capital‐constrained retailer. We investigate a unique financing approach involving a blend of bank loans and supplier equity investment to support the retailer's operational (procurement and marketing) activities. Analyzing the equilibrium strategies under both symmetric and asymmetric information settings yields intriguing insights. In the case of symmetric information, we find that the retailer's equilibrium order quantity decreases with the potential market size under hybrid financing, contrary to traditional notions. When asymmetric information is present, a higher acceptance of supplier equity investment by the retailer tends to lead to order quantity distortion downward, increasing signaling costs. Furthermore, a greater proportion of supplier equity investment prompts the retailer to order more products, ultimately boosting profits for both the retailer and supplier. This suggests that supplier equity investment can enhance supply chain efficiency and alleviate the double marginalization effect.

The Stochastic Evolution Game of Knowledge-Sharing Incentive in Virtual Communities under Intelligent Recommendation Systems

To effectively solve the issue of unsmooth knowledge sharing in virtual communities under intelligent recommendation systems, we analyzed the impact of key factors on the strategy selection and evolution path in different scenarios.Based on the principles of bounded rationality and benefit maximization, we consider the principles of evolutionary game theory and the influence of random interference. A random evolutionary game model is constructed to analyze strategy selection in the process of knowledge sharing incentives between virtual community platforms and users. We obtained the evolutionary equilibrium strategies under different parameter restrictions and analyzed the evolutionary stability of the dynamic game process of knowledge sharing incentives.The research shows that interference from random factors affects both the speed and the trend of strategy evolution in virtual community platforms and users. In order to improve the enthusiasm of users to share, virtual community need to increase the proportion of users with positive feedback, improve the recommendation incentive mechanism, and reduce the user loss coefficient. Based on the above research conclusions, some countermeasures and suggestions for improving the performance of virtual community knowledge sharing under intelligent recommendation systems are proposed, which provides theoretical guidance for knowledge sharing among virtual community members.

Constructive Approximate Nash Equilibrium for In-Orbit Target Enclosing with Collision Avoidance and Full-state Constraint via Nonzero-Sum Differential Games

The problem of in-orbit cooperative target enclosing involving N thrust-limited satellites under collision avoidance and maneuver amplitude constraints is studied. In order to find global optimal trajectories for target enclosing task with all constraints above, by integrating the collision threat and maneuver boundaries into a novel nonlinear cost functional, the studied target enclosing problem is described as a nonlinear nonzero-sum differential game. Further, to avoid iterative calculations caused by traditional nonlinear-game-solving methods, an approximate solution which can be constructed directly is designed. Then the approximate Nash equilibrium strategies can be educed by the constructive approximate solution for the proposed nonzero-sum game. Analysis shows that the proposed control strategies can asymptotically approach the exact one and can ensure a zero-error tracking of the enclosing configuration. Simulation results illustrate lower time costs and better enclosing accuracy while the collision avoidance and maneuver amplitude constraints are satisfied simultaneously.

Impact of fairness concerns on resource-sharing decisions: A comparative analysis using evolutionary game models in manufacturing enterprises

In recent years, the resource-sharing model has developed rapidly, and manufacturing enterprises have paid more attention to profit distribution and resource investment. Studying the role of fairness concern behaviour in enterprise resource-sharing decisions can provide strategic references for enterprises to implement resource-sharing. This article considers the fairness concern behaviour of resource-sharing enterprises and constructs two symmetric evolutionary game models for resource-sharing. Based on the resource-sharing strategy when the enterprise is fair and neutral, a comparative study is conducted on the impact of fairness concern behaviour on the resource-sharing equilibrium strategy. MATLAB is used for numerical simulation. The analysis results indicate that: (1) the system cost coefficient, information level coefficient, information loss coefficient, resource conversion ability coefficient, resource collaboration ability coefficient, and penalty factor all have an impact on the strategic evolution results of both parties in the game enterprise, (2) fairness concerns include heterogeneity, directionality, and reinforcement, which affect the resource-sharing strategies of enterprises. This study provides a reference for shared decision-making in manufacturing enterprises and provides recommendations for their business development.

A mean field game approach to equilibrium consumption under external habit formation

This paper studies the equilibrium consumption under external habit formation in a large population of agents. We first formulate problems under two types of conventional habit formation preferences, namely linear and multiplicative external habit formation, in a mean field game framework. In a log-normal market model with the asset specialization, we characterize one mean field equilibrium in analytical form in each problem, allowing us to understand some quantitative properties of the equilibrium strategy and conclude some financial implications caused by consumption habits from a mean-field perspective. In each problem with n agents, we construct an approximate Nash equilibrium for the n-player game using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained.

Online discrimination-correction subnet for background suppression and dynamic template updating in Siamese visual tracking

The offline Siamese tracking methods have recently attracted much attention due to their impressive performance on speed and accuracy. However, they ignore the target and background information during tracking, thus lacking sufficient discrimination ability to handle complex background interference, and cannot robustly adapt to sharp appearance variations in challenging situations, such as scale variation, rotation, occlusion, and background clutter. To address the drawbacks above, we propose an online discrimination-correction subnet, which discriminates and corrects the tracking results obtained by the Siamese tracker through online learning, and further guides the template update. Firstly, a feature refinement module is designed to enhance the discriminative ability of features, which compresses and combines target features based on the importance of feature channels to obtain target-specific features. On this basis, an online discriminator module is proposed to learn the decision boundary between target and background through samples collected online to suppress background interference. In addition, a sample equilibrium strategy is proposed to alleviate the imbalance in the distribution of positive and negative samples during online training. Finally, to handle sharp target appearance variations, a robust template updating strategy is proposed to screen high-quality historical samples to generate dynamic templates. To evaluate the generalization ability and effectiveness of our method, we apply it to four classical Siamese trackers, namely SiamFC, SiamRPN++, SiamCAR, and TransT. Extensive experiments on seven challenging benchmarks demonstrate that our method significantly improves the baseline methods and achieves outstanding performance compared with state-of-the-art trackers.

Strict liability versus negligence in the case of data breach

This study compares the efficiency of the strict liability and negligence rules in the case of a data breach. Contrary to standard results, we demonstrate that the strict liability rule cannot induce the efficient activity and care levels of a data controller. This is mainly due to possible positive externalities from data breaches, unlike in usual tort cases. We show that the negligence rule is more efficient than the strict liability rule if the positive externality is sufficiently large. The main insight is carried over to the case where a data controller uses a data processor to process personal information before selling it in the market. If hackers are explicitly introduced into the model, the care level of the data controller increases with the hacking activity, whereas the latter level decreases with the former. In this model, if the hacker’s gain is sufficiently small, the negligence rule can be made more efficient by adjusting due care to a harsher level than the equilibrium care level under strict liability to reduce hacking activity, although a pure strategy equilibrium may not exist for some due care levels.

Service provision decisions of competitive manufacturers: From service spillover perspective

This paper investigates competing manufacturers’ strategic choice of service provision in a two-level supply chain composed two manufacturers and one common retailer. Our results indicate that the strategy that two competing manufacturers provide services is always the dominant choice, and two competing manufacturers could have the highest profit in that case. But when only one of them provides services, the result is related to the potential market size, the unit service cost coefficient and the service spillover intensity. Finally, through the cost sharing and quantity competition extensions, we find the Pareto regions of cost sharing under the equilibrium strategy, and there will be multiple Nash equilibrium regions under the quantity competition.

On priority-proportional payments in financial networks

We study financial systems from a game-theoretic standpoint. A financial system is represented by a network, where nodes correspond to banks, and directed labeled edges correspond to debt contracts between them. The existence of cycles in the network indicates that a payment of a bank to one of its lenders might affect the bank's incoming payments. So, if a bank cannot fully repay its debt, then the exact payments it makes to each of its lenders can affect the cash inflow back to itself. We naturally assume that the banks are interested in their financial well-being (utility) which is aligned with the amount of incoming payments they receive from the network. This defines a game among the banks, that can be seen as utility-maximizing agents who strategize over their payments.We introduce a class of financial network games that arise under some natural payment strategies called priority-proportional payments. We compute valid payment profiles for fixed payment strategies and we investigate existence and (in)efficiency of equilibrium strategies, under different variations of the game that capture several financial aspects that commonly arise in practice. We conclude with examining the computational complexity of a variety of related problems.

Foreign Direct Investment and Technology Licensing in a Polluting Industry

We consider a firm’s incentive for foreign direct investment (FDI) and international technology licensing in a polluting industry. We explain the rationale and the welfare implications of complementarity between FDI and licensing, i.e., the firm’s strategy of “FDI and licensing” (FL), which is empirically relevant but ignored in the literature. When the environmental tax cannot be committed, the firm adopts the licensing strategy if the pollution intensity is not high, and the licensing strategy may create lower consumer surplus and welfare compared to both FDI and FL. However, if the pollution intensity is high, the firm undertakes FL, which provide higher consumer surplus and welfare compared to both licensing and FDI. When the government can commit to the environmental tax, the firm always prefers FL. The host-country welfare is higher but the consumer surplus and world welfare may be lower under the committed tax policy compared to the non-committed tax policy. These results hold under Cournot competition and Stackelberg competition. We further show that FL can be the equilibrium strategy of the foreign firm if there is fixed-fee licensing instead of a two-part tariff licensing, which is considered in the main analysis.

Tripartite Evolutionary Game Analysis of Product Quality Supervision in Live-Streaming E-Commerce

With the rapid development of information technology, live-streaming e-commerce has risen rapidly as a new business model. However, product quality problems that exist in the development of live-streaming e-commerce continue to emerge. The influence of strategic interactions between social media influencers, live-streaming e-commerce platforms, and consumers on product quality deserves to be studied. Therefore, this paper constructs a tripartite game model of “social media influencers–the live-streaming e-commerce platform–consumers” and analyzes the dynamic evolution process of the strategy selection among subjects and influencing factors by using evolutionary game theory. This study shows that products with high functional value are more likely to stimulate consumer rights protection behavior, prompting social media influencers to shift from lax to strict quality control. But when the emotional value is high, consumers are more inclined to give up on defending their rights, which leads to the maintenance of lax quality control, and the platform supervision will be weakened accordingly. Moreover, less quality differences motivate social media influencers to choose lax quality control. An increase in quality differences will promote a shift from an equilibrium strategy to strict quality control. However, if the penalty of the platforms is not strong enough, this strategic shift will not happen. In addition, a high percentage of platform commissions can encourage influencers to implement strict quality control, while platforms can maintain weak supervision. This study’s findings provide valuable guidance for understanding and managing product quality issues in live-streaming e-commerce. In the future, the government will be considered a new player in the game in studying the impact of its policies on product quality in live-streaming e-commerce.

Adjustment strategies and chaos in duopoly supply chains: The impacts of carbon trading markets and emission reduction policies

Low-carbon policies serve as a core incentive mechanism to promote carbon reduction in duopoly supply chains. However, their directive impact may cause product prices and carbon emission adjustment speeds to accelerate too quickly, thereby triggering market instability. Current research is noticeably lacking in discussions on optimal configurations of supply chain management strategies and policy implementation under market equilibrium conditions. Therefore, this paper utilizes game theory and chaos theory to explore the dynamic operational strategies and optimal profits of duopoly supply chains under a single carbon trading mechanism and considering carbon reduction incentives. The findings indicate: (1) Price adjustment parameters significantly affect both parties' equilibrium strategies and system stability; (2) An increase in carbon prices and carbon reduction incentive intensity both narrow the stable areas for pricing and reduction strategies; (3) Both manufacturers and remanufacturers experience higher optimal pricing, reduced carbon reductions on their part, and more carbon reductions on the part of their counterparts due to the escalating costs of carbon reduction; (4) While enhancing carbon reduction incentives significantly aids both parties in achieving carbon reductions, as the reduction effect gradually diminishes, it also compresses their profit margins, whereas an increase in carbon quotas can linearly enhance business profits.