Irrational behaviour-induced suppression, enhancement and oscillations of voluntary vaccination: A stochastic model with delays

Uplink/downlink (UL/DL) decoupled access has emerged as a promising paradigm for heterogeneous cellular vehicle-to-everything (C-V2X) networks in beyond 5G (B5G) and 6G systems. In multi-operator scenarios, wireless service provider (WSP) selection becomes critical for vehicles to ensure communication quality while minimizing costs. This paper investigates the performance analysis and WSP selection problem in UL/DL decoupled access C-V2X networks. We derive tractable expressions for spectral efficiency of both UL and DL using stochastic geometry, considering three decoupled access cases where UL and DL independently associate with macro base stations (MBSs) or small base stations (SBSs). We formulate a hierarchical game framework combining evolutionary game for vehicle WSP selection and non-cooperative game for WSP bandwidth allocation. An evolutionary game algorithm is proposed to reach the equilibrium, and the uniqueness of Nash equilibrium in bandwidth allocation is proved. Extensive simulations validate the analytical results and demonstrate the convergence and stability of the proposed game framework.

As the integrated energy market evolves toward a multi-stakeholder coexistence model, balancing economic efficiency, user well-being, and system-level sustainability among interacting stakeholders has become a key challenge, particularly in the rapidly developing regional integrated energy markets in China. Thus, to satisfy user comfort and energy substitution requirements while achieving cost-effective electricity and heating supply, this study proposes a Stackelberg game-based market trading framework involving an integrated energy producer (IEP), an integrated energy operator (IEO), and a load aggregator (LA). First, the integrated energy market framework and transaction modes are established, and the profit models of IEP and IEO are formulated. Considering users’ energy substitution behavior, user comfort is quantified to explicitly reflect user welfare in market decision making, and a consumer surplus model is developed for LA participating in market transactions. Second, a Stackelberg game framework is constructed to coordinate the strategies of all participants by incorporating source–load energy flows, and the equilibrium solution is proven to be unique and solvable using quadratic programming. Finally, a case study based on historical data from Hebei Province, China, is conducted to validate the proposed strategy. The results demonstrate that the proposed method effectively coordinates the interests of all stakeholders, enhances demand response capability without reducing user comfort, and improves economic benefits for both supply and demand sides in regional integrated energy markets.

This paper investigates the problem of contract coordination in a two-tier multi-unit auction supply chain consisting of a seller and an auction house. We theoretically show that the conventional commission-based mechanism distorts the transmission of demand information from the demand side to the supply side, thereby preventing effective supply chain coordination. In contrast, guaranteed auction contracts can achieve coordination under both cooperative and non-cooperative game frameworks. Under the cooperative game setting, profits are allocated according to a Nash bargaining solution, in which each party receives its disagreement payoff and a bargaining-power-weighted share of the surplus, with risks and returns being allocated symmetrically. Under the non-cooperative game setting, the supply chain leader can appropriate a larger share of the total profit while bearing relatively lower risk. These results indicate that, as the supply chain leader, the auction house can select different cooperation modes under guaranteed auction contracts according to its bargaining position, but profit allocation should be benchmarked against the cooperative game outcome in order to enhance the long-term competitiveness and stability of the supply chain.

We investigate cybersecurity investment strategies in scale-free supply chain networks where risk propagates directly and indirectly through data connections. A stochastic game framework is developed, incorporating a Gordon–Loeb direct attack function and multi-path cumulative indirect risk propagation. A collaborative defense coalition with joint investment pooling and shared liability is introduced to internalise externalities. An iterative best-response algorithm combined with dynamic programming is proposed to compute approximate Nash equilibria. Theoretical propositions characterise investment monotonicity, spillover effects, and the non-trivial impact of collaboration. Numerical experiments on a representative network reveal that collaborative defense does not always reduce total cost, especially when investment caps bind. The findings offer actionable insights for designing resilient cybersecurity strategies in interconnected supply chains.

To address the challenges of low-carbon economic optimization and collaborative management for multiple Virtual Power Plants (VPPs), this paper proposes a low-carbon economic optimization and collaborative management method based on a Stackelberg game framework. Firstly, a Stackelberg game model is constructed with the Distribution System Operator (DSO) as the leader and multiple VPPs as followers. The leader (DSO) guides the followers’ behavior through dynamic pricing strategies to maximize its own utility. Meanwhile, the followers (VPPs) develop energy management strategies to minimize their individual costs, taking into account factors such as energy transaction costs, fuel costs, carbon trading costs, operation and maintenance (O&M) costs, compensation costs, and renewable energy generation revenues. Furthermore, the strategy spaces of all participants are defined, and an optimization model is established subjected to constraints including energy balance, energy storage operation, power conversion, and flexible load response. The CPLEX solver and Nonlinear-based Chaotic Harris Hawks Optimization (NCHHO) algorithm are employed to solve the proposed game model. Simulation results demonstrate that the proposed method effectively facilitates collaboration between the DSO and multiple VPPs. While ensuring the safe operation of the system, it balances the profit between the DSO and VPPs, and incentivizes renewable energy consumption and indirect carbon reduction, thereby validating the effectiveness and superiority of the method and providing reliable technical support for the low-carbon collaborative operation of multiple VPPs.

Uncertainty is prevalent in game-theoretical models, which may occur due to numerous factors such as incomplete information, fuzziness in preference structures and external environment fluctuations. The framework of games with set payoffs provides a potent means to capture such uncertainties. This paper focuses on parametric generalized set payoffs games and investigates their equilibrium properties through the null set concept. To this end, a weak set order relation with respect to the null set will be used to define the equilibrium concept for generalized set payoffs games. Based on the continuity and concavity settings imposed on the set-valued payoff functions, we prove the equilibrium existence for such a game. Subsequently, we define the notion of approximating sequences for parametric generalized set payoffs games and derive sufficient conditions to ensure their well-posedness and generalized well-posedness. Based on the parametric games, sufficient conditions for ensuring upper and lower semicontinuity, as well as compactness, of equilibrium mappings are also delivered. Illustrative examples are provided to validate the developed conclusions.

ABSTRACT In the paper, a novel resilient model predictive control (MPC) strategy is proposed based on a two‐step game framework for discrete‐time nonlinear cyber‐physical systems (CPSs) under false data injection (FDI) attacks. Firstly, considering the controller's limited capacity to process data at each sampling instant, a two‐step game‐based security framework is designed to adaptively allocate computation and protection resources, ensuring that the transmitted key control input signals can withstand FDI attacks while maximizing the system performance improvement. Secondly, a resilient strategy is proposed to identify the positions of the transmitted key control input signals and further generate a backup control input sequence based on these key control input signals. By combining the game framework with the resilient method, the controller can effectively minimize resource consumption and improve the efficiency of computation resource utilization. Combining these features, a novel resilient MPC algorithm is developed to safeguard the CPS from FDI attacks. Furthermore, the iterative feasibility of the proposed algorithm and the closed‐loop stability of the controlled CPS under FDI attacks are rigorously demonstrated. Finally, the effectiveness of the proposed method is validated through a simulation comparison.

Autonomous Mobility on Demand (AMoD) fleets are emerging as the application of the sharing economy in the transportation sector. Their success offers significant opportunities for decarbonization within the transportation sector. This paper proposes a dual-pricing mechanism for AMoD fleets based on a non-cooperative Stackelberg game framework. In the proposed framework, the Charging Station Operators (CSOs) set the charging prices while the AMoD operator determines the transportation prices. This dual-pricing strategy collaboratively navigates the AMoD fleets, thereby fostering the utilization of photovoltaic resources. To account for the uncertainty in photovoltaic generation, the pricing interaction is formulated as a distributionally robust game, and a generalized Stackelberg equilibrium computing algorithm is developed. The proposed dual-pricing mechanism explicitly enhances the coordination between AMoD operations and power systems by enabling spatial– temporal charging load shifting and improving photovoltaic utilization, thereby increasing the overall operational efficiency of the coupled transportation–power system. Numerical case studies validate the effectiveness of the proposed framework.

With the advancement in battery technology, electric vehicles have emerged as a feasible alternative for ride-sourcing. In various cities worldwide, policies promoting ride-sourcing electrification have been implemented. Despite these efforts, significant challenges remain, particularly with respect to the cooperative mechanism among various stakeholders. To address this issue, this study examines the motivations for ride-sourcing electrification through a tripartite evolutionary game framework, consisting of the government, ride-sourcing platforms, and ride-sourcing drivers. The basic model is constructed by considering factors such as social benefits, environmental benefits, subsidies, penalties, drivers’ commission rates, and transaction revenues. On the basis of this, the evolutionary stable strategies of each stakeholder and the system are analyzed. Further, a numerical study is conducted. The results indicate that the strategy of each stakeholder is influenced by the strategies of the others. Additionally, to promote the electrification of ride-sourcing more effectively, the government should consider both social and environmental benefits, as well as the balance between subsidies and penalties. For ride-sourcing platforms, attention should focus on the additional benefits resulting from electrification externalities. With respect to ride-sourcing drivers, their strategies are jointly influenced by factors such as revenues and commission rates. Based on these findings, this study offers valuable policy implications for both policymakers and platforms.

With the continuous increase in the penetration rate of renewable energy sources, the uncertainty of new energy output has brought significant risks and challenges to the planning strategy of integrated energy systems. Meanwhile, power grid operators and heat network operators, belonging to different stakeholder entities, exhibit complex cooperative-competitive game relationships, making it difficult to balance the interests of all parties. To address this issue, this paper proposes a game theory and optimal planning strategy for electricity-heat multiple heterogeneous energy systems based on a deep temporal clustering method from the perspective of different stakeholders. Firstly, typical scenarios of renewable energy output are generated through the deep temporal clustering method. Simultaneously, the charging and discharging behaviors of energy storage devices are utilized to assist the distribution system in new energy consumption. This paper incorporates battery life degradation costs into the objective function on the power grid side to achieve accurate accounting of energy storage device dispatch expenses. Additionally, an optimal dispatch model is established on the heat network side, upon which a game framework for multiple heterogeneous energy systems is constructed. The construction capacity and installation location of each flexible device can be determined through planning decisions in typical multi-scenario situations. Considering the non-convex and nonlinear characteristics of the model, this paper employs an improved firefly algorithm to achieve optimal solution search and rapid convergence. Finally, the effectiveness and feasibility of the proposed method are demonstrated through a case study of an electricity-heat energy system.

In the context of increasingly intense competition among digital platforms, the strategic pricing behavior of two-sided media platforms has attracted considerable academic attention. The pricing model for two-sided platforms proposed by Amaldoss et al. provides a theoretical foundation for understanding the interaction among consumer heterogeneity, multi-homing behavior, and advertising strategies. However, a series of idealized assumptions within the model present limitations when applied to real-world scenarios. This paper offers a systematic review and critical analysis of the model, identifying key issues in aspects such as consumer representation, advertiser behavior, platform strategy space, and market structure assumptions. Based on these insights, several extensions are proposed, including the introduction of continuous advertising aversion levels, endogenous attention allocation mechanisms, advertiser heterogeneity and budget constraints, asymmetric platform capabilities, and a dynamic game framework. Through structural modifications and mechanism enhancements, the model’s behavioral realism and practical explanatory power are significantly improved, offering valuable references for the development of platform pricing theory and its practical implementation.

There is a growing need for accessible and engaging rehabilitation tools for individuals with neurodevelopmental disorders such as Cerebral palsy (CP), Down syndrome (DS), and Autism spectrum disorder (ASD). Serious games offer a promising approach, yet few are tailor-made to meet the therapeutic demands of these populations. A tailor-made, non-immersive virtual reality (VR) serious games framework featuring a basketball task was developed, with therapist-controlled modules for customization and monitoring. Twenty-eight participants (CP: 14; DS: 7; ASD: 7) completed the game across eight sessions, grouped into three practice phases: an initial session, an early adaptation phase, and a consolidated practice phase. Performance metrics included accuracy, reaction time, and number of victories. All groups improved performance across phases, with accuracy increasing significantly in central (p = 0.005) and total positions (p = 0.007). The number of victories also increased from the initial to the early adaptation phase (p = 0.019) and from the initial to the consolidated practice phase (p = 0.008). Participants with ASD showed significantly higher accuracy than the DS group, while CP and DS participants showed a temporary increase in reaction time during the early adaptation phase, followed by a reduction in the consolidated phase, suggesting task adaptation. These findings support the feasibility and short-term effectiveness of a modular, tailor-made serious games platform for telerehabilitation.

ABSTRACT Globalization has significantly amplified the risk of supply chain disruptions, posing serious threats to operational stability. While e‐commerce platforms facilitate information sharing among supply chain members, the precise strategic value of such sharing under disruption risk remains insufficiently explored, particularly across different distribution channels. This research examines a two‐tier supply chain comprising a manufacturer with potential supply disruptions and an e‐commerce platform. The interaction is modeled using a Stackelberg game framework under two distinct sales configurations: without and with manufacturer encroachment. The analysis reveals that the value of information sharing is highly sensitive to several factors, including the sales channel structure, the pattern of demand fluctuations, the manufacturer's efficiency in improving resilience, the intensity of channel competition, and the platform's revenue‐sharing rate. Under the wholesale model, the platform prefers (not) to share negative (positive) demand information. In contrast, under the hybrid model, the platform's sharing strategy becomes complex, which is jointly moderated by multiple parameters. Notably, under disruption‐induced capacity constraints, a higher ex‐ante capacity commitment to the wholesale channel paradoxically reduces realized order volumes, as the manufacturer raises wholesale prices to compensate for reduced allocation flexibility. The manufacturer's encroachment decision is fundamentally a trade‐off between fixed entry costs and anticipated incremental gains. Both elevated revenue‐sharing rates and intensified channel competition are found to suppress the manufacturer's incentive to encroach. Finally, extensions considering endogenous allocation and a signaling game framework demonstrate that the manufacturer's ability to infer demand signals enhances wholesale profitability, thereby further mitigating the motivation for channel encroachment.

Background: The majority of the funding for the New Rural Cooperative Medical System (NCMS) is derived from fiscal subsidies, comprising central transfer payments and local fiscal matching subsidies. Local governments' strategic behavior in response to central transfer payments may further impact NCMS compensation spending and medical economic risks. Methodology: Accordingly, this paper investigates, from both theoretical and empirical perspectives, the impact pathways through which local fiscal matching subsidies influence the medical economic risks faced by insured rural households, with central transfer payments serving as a moderating factor. This paper constructs a dynamic game framework involving the central government, local governments, and household sectors. It further applies a mediation effect model and related econometric methods to conduct empirical analysis using 87,630 observations from the China Family Panel Studies (CFPS). Results: The results show that, first, local fiscal matching subsidies significantly reduce catastrophic health expenditures for rural households under the income effect of central transfer payments. However, under the substitution effect, the opposite occurs, as local governments adopt non-cooperative strategies in response to central transfer payments. Second, these impacts exhibit regional heterogeneity, with stronger effects in eastern regions, regions with more developed secondary industries, and regions with higher fiscal self-sufficiency rates. Third, local fiscal matching subsidies influence medical economic risks through compensation spending, under the moderating role of central transfer payments. Conclusions: This paper provides a novel perspective on why the NCMS struggles to provide effective protection, thereby enriching the existing literature. Furthermore, it provides policy guidance for fiscal and healthcare reforms in countries with similar contexts to China. Based on these insights, we argue that, during the future integration process of the Basic Medical Insurance for Urban and Rural Residents, clear boundaries should be defined for local fiscal matching subsidies, and the moderating role of central transfer payments should be strategically leveraged.

ABSTRACT We study a Cournot duopoly with socially responsible (CSR) firms and unions that value CSR objectives. Applying an innovation game framework, we examine how CSR engagement and union attitudes influence firms’ innovation decisions. The model demonstrates that while CSR activities boost profits for all firms, the innovator's profits increase more, creating a clear incentive to innovate. This incentive persists with unions, but only if they disregard the firm's CSR commitments. If, however, unions are sufficiently concerned with CSR, they can discourage innovation. Thus, CSR presents a dual – or ‘two-faced Janus’ – effect on a firm's innovative impetus.

BackgroundChildren with autism spectrum disorder (ASD) exhibit cognitive, motor, and social difficulties that affect engagement, causing developmental delays, behavioral challenges, and obesity—interrelated concerns in daily functioning and well-being. Although interactive interventions have incorporated physical activity, they often rely on limited physical involvement and lack iterative, expert-informed design, as built on pre-existing game frameworks. Physical activity is often operationalized as constrained input (eg, gestures or in-place actions) rather than exertion-intensive, whole-body exercise, and design guidance for adapting exercise content under ASD-oriented safety and cognitive-sensory constraints remains limited. These limitations highlight the need for exergames that promote sustained, full-body participation aligned with developmental goals, motivating formative, co-design with expertise and initial field testing in this population.ObjectiveWe aim to iteratively design exercise-based serious games (SGs) for children with ASD through a structured, expert-informed co-design process involving 21 professionals across special education, adapted physical education, and human-computer interaction, and to examine feasibility and use contexts through an exploratory multiple-case pilot study.MethodsWe derived serious exergames using 4 design methods—stakeholder interview, concept mapping, creative matrix, and visualize the vote. Two exergames—“Fruit Sorting Run” and “Hazard Avoiding Ride”—were developed, integrating full-body running and cycling movements into goal-directed tasks under ASD-oriented constraints. We conducted a multiple-case pilot with 3 children with ASD. During gameplay, caregivers labeled engagement using a binary input interface, and we conducted postsession caregiver interviews to capture complementary observations.ResultsEngagement in both exergames tended to increase over normalized time. Generalized estimating equations with a logit link and an autoregressive working correlation of order 1 (AR1), including participant indicators, showed a statistically significant association between normalized time and engagement in Fruit Sorting Run (per 0.1 increase: β=0.48; odds ratio 1.62, 95% CI 1.09-2.38; P=.02) and Hazard Avoiding Ride (per 0.1 increase: β=0.66; odds ratio 1.93, 95% CI 1.04-3.60, P=.04). Caregiver interviews reinforced these findings, reporting increased attention, motivation, and enjoyment across both activities.ConclusionsThe findings support the applicability of an expert-informed design approach and the viability of the resulting exergames, integrating goal-directed physical activity, virtual agent–based prompting, and stakeholder-informed considerations such as motor-cognitive alignment, interactive scaffolding, and support for daily living skills. Distinct from prior SG approaches that operationalize physical activity through discrete gestures or in-place interactions, the proposed exergames embed sustained, exertion-intensive, whole-body movement within structured gameplay. Within this exploratory multiple-case pilot, engagement trajectories tended to increase over time. These preliminary observations provide an initial basis for a testable hypothesis that exertion-intensive, full-body SGs with virtual agent–based prompting may be associated with increasing engagement over time, meriting further examination in larger samples and applied educational and therapeutic contexts.

A learning and communication-based coordination framework for multi-spacecraft orbital games with impulsive maneuvers

A unified and efficient training framework for open-ended non-transitive games.

Utilizing a panel dataset from OECD countries, this study unveils new evidence suggesting that the centralization of wage bargaining plays a significant role in mitigating Political Budget Cycles. To explain this empirical finding, the paper introduces a political economy model based on a policy game framework, encompassing three key agents: (i) an opportunistic government that decides on the level of budget deficits with the objective of enhancing its reelection prospects, (ii) workers/voters who decide on their sectoral affiliations, and (iii) unions that independently negotiate wages with firms. In this model, the opportunistic government has an incentive to run a budget deficit to favor the median voter, who is affiliated with non-tradable sectors. The mechanism emerges from the impact of debt-financed public spending on relative prices, and consequently, on relative wages between non-tradable and tradable sectors. Wage centralization mitigates the political incentive of opportunistic governments by attenuating the responsiveness of sectoral wages to sectoral prices, thereby pushing down budget deficits towards a socially more optimal level.