Game Framework Research Articles

Optimization Analysis of Smart Energy Systems in the Fresh Supply Chain Based on Differential Games

The energy issue has gradually become a major focus of strategic competition among major nations in the contemporary world. Achieving a balance between energy, cost, and ecology is crucial, particularly in specific contexts. As one of the critical factors influencing global climate, carbon emissions have consistently been a green indicator of concern for countries worldwide. This paper addresses optimizing energy costs in the cold chain transportation of the fresh supply chain to obtain a model with low carbon emissions and transportation costs. Initially, the paper explores the equilibrium between energy and cost optimization using the theoretical framework of differential games in game theory. Building upon this, an intelligent energy system is proposed, and a basic model for constructing a smart grid is provided based on commonly used electric power. Using this as the foundational concept, a game model is constructed, considering the conflicting objectives of cost minimization, time efficiency, and energy conservation in addressing the primary issue of energy savings in the fresh supply chain, specifically the transportation path optimization problem. Compared to traditional models, the model presented in this paper reduces the scheduling of two refrigerated trucks. By optimizing this model, the transportation path's length is shortened by 5.50%, the carbon emission is decreased by 8.9%, and the model's overall cost is reduced by 4.94%. This study presents a game model that may efficiently optimize the fresh product transportation chain, reducing carbon emissions and expenses. The model has certain practical applications and serves as a guide.

Solar–Hydrogen-Storage Integrated Electric Vehicle Charging Stations with Demand-Side Management and Social Welfare Maximization

The reliable operation of a power system requires a real-time balance between supply and demand. However, it is difficult to achieve this balance solely by relying on supply-side regulation. Therefore, it is necessary to cooperate with effective demand-side management, which is a key strategy within smart grid systems, encouraging end-users to actively engage and optimize their electricity usage. This paper proposes a novel bi-level optimization model for integrating solar, hydrogen, and battery storage systems with charging stations (SHS-EVCSs) to maximize social welfare. The first level employs a non-cooperative game theory model for each individual EVCS to minimize capital and operational costs. The second level uses a cooperative game framework with an internal management system to optimize energy transactions among multiple EVCSs while considering EV owners’ economic interests. A Markov decision process models uncertainties in EV charging times, and Monte Carlo simulations predict charging demand. Real-time electricity pricing based on the dual theory enables demand-side management strategies like peak shaving and valley filling. Case studies demonstrate the model’s effectiveness in reducing peak loads, balancing energy utilization, and enhancing overall system efficiency and sustainability through optimized renewable integration, energy storage, EV charging coordination, social welfare maximization, and cost minimization. The proposed approach offers a promising pathway toward sustainable energy infrastructure by harmonizing renewable sources, storage technologies, EV charging demands, and societal benefits.

Cultural rice fields in the wave of climate change: a multilateral evolutionary game framework for adaptive management of agricultural heritage systems

Agricultural Heritage Systems (AHS) are pivotal in preserving rich agricultural production experience and traditional culture, as well as in maintaining biodiversity and promoting sustainable development in agriculture and rural economies. However, climate change poses significant threats to these systems, such as ecological degradation, biodiversity loss, and shifts in agricultural production patterns. This study, grounded in theories of information asymmetry and bounded rationality, constructs evolutionary game models for adaptive management of AHS under market mechanisms and government guidance. By employing stability analysis and numerical simulation with Delay Differential Equations (DDE) that consider historical delays, and through sensitivity analysis, this research delves into the strategic evolutionary outcomes of stakeholders under various scenarios. It aims to provide theoretical insights and policy recommendations for the dynamic protection and adaptive management of AHS in the face of climate change. The findings indicate that the public goods nature of AHS, alongside externalities and information asymmetry, leads to market failure. Sole reliance on autonomous actions by farmers and meteorological departments is insufficient for optimal resource allocation and effective protection. Government intervention, through regulatory and incentive measures, can effectively mitigate market failures and steer adaptive management of AHS towards efficiency and sustainability. Moreover, the study identifies key factors for adaptive management, such as enhancing stakeholders’ initial willingness to participate, reducing the costs of adapting to climate change, optimizing cooperative benefit distribution mechanisms, and increasing the profitability of resource cooperation. Sensitivity analysis of government subsidies and penalty mechanisms further reveals the complex and critical role these policy tools play in fostering stakeholder engagement. Based on these findings, the study recommends enhancing initial participation willingness, controlling transformation costs to alleviate economic burdens, optimizing benefit distribution mechanisms to boost cooperative resource profitability, and establishing dynamic subsidy and penalty mechanisms for optimal resource allocation. The theoretical and practical contributions of this research lie in applying theories of information asymmetry and bounded rationality to the adaptive management of AHS under climate change, enriching the theoretical framework in this field, and providing scientific decision-making support for policymakers. By demonstrating an effective path for AHS protection through combined government and market mechanisms in the context of global climate change, this research holds significant theoretical and practical implications for enhancing the efficiency of adaptive management of AHS, protecting, and inheriting valuable agricultural cultural heritage.

Adaptive mixed reality robotic games for personalized consumer robot entertainment

The Adaptive Mixed Reality Robot Games (AMRRG) framework represents an innovative approach to integrating consumer robots into public spaces for personalized and engaging entertainment. AMRRG uses a combination of mixed reality headsets, robot movement, and interactive objects. These responsive entertainment environments need a new way to tell their story. Admixing game mechanics algorithm utilizes the world’s most advanced depth perception, computer vision, and simultaneous mapping and localization (SLAM) to enable effective distinguishing between player spaces, mixed reality areas, and robot paths for safe interaction. Reinforcement learning enables real-time adaptation of game difficulty and gameplay mechanics as players react to it. At 35 % higher than traditional video-game installations in a 5 m × 5 m environment accommodating up to 20 people, adaptive algorithms recorded efficiency values of 92 % and responsiveness of 98 %. The AMRRG framework brings home consumer robot platforms to deliver a happy gaming experience. Future research will explore the potential of AMRRG beyond simple adaptation, extending its use to therapy and education.

Low-carbon optimal scheduling of park-integrated energy system based on bidirectional Stackelberg-Nash game theory

Multi-stakeholder participation is crucial in facilitating the development of park-integrated energy systems (PIES). Balancing the diverse interests of various stakeholders, each with its distinct requirements presents a notable challenge. Concurrently, the model's complexity increases due to the engagement of various stakeholders, posing challenges to its resolution through traditional methods. In this context, this paper aims to investigate an optimal scheduling model that incorporates shared energy storage (SES) system, microgrids operator (MGO), electric vehicles station (EVS), and user aggregator (UA) with multiple prosumers. To comprehensively address the interests of all stakeholders, this study introduces a tri-level optimization model. The proposed model integrates a bidirectional Stackelberg-Nash game framework, in which the SES acts as the leader, the MGO acts as the secondary leader, and the UA-EVS acts as the followers while allocating benefits based on the asymmetric Nash bargaining theory. The Stackelberg game model between MGO and UA-EVS is analyzed using the Karush-Kuhn-Tucker (KKT) condition, while the Stackelberg game model between SES and MGO is resolved using the bisection method. Meanwhile, the Nash bargaining method among users is solved using the alternating direction method of multipliers (ADMM) technique. The analysis indicates that the proposed strategy can reduce PIES's costs and carbon emissions, yielding a win-win situation for all stakeholders.

A hierarchical game framework for peer-to-peer energy trading in distribution networks considering the participation of prosumers

The advent of the peer-to-peer energy trading has dramatically altered the conventional dynamics of distribution networks. Prosumers, managing independently and engaging in peer-to-peer (P2P) energy exchanges, introduce critical challenges for the economical and secure operations of these networks. This research presents a hierarchical framework designed to manage P2P energy interactions between prosumers and to facilitate flexible operation within the distribution network at the substation level. The upper layer of the model aims to stabilize market prices within the distribution framework, while the lower layer establishes a P2P energy trading platform that upholds fairness and safeguards the privacy of the prosumer participants. A fixed-point mapping approach is utilized to assess the interactions between market stabilization efforts and prosumer bidding strategies within this framework. Through simulations, we illustrate the logical soundness and effectiveness of our proposed model and approach. The findings indicate that the proposed model and the energy trading framework could substantially improve the overall welfare of all stakeholders involved.

Research on dynamic game operation behavior of multi‐oligopoly car‐sharing operators considering off‐peak pricing factors

AbstractIn the practical evolution of shared vehicle systems, numerous societal factors come into play, such as inadequate parking infrastructure, battery capacity, and the budget for technological improvement. This study integrates the operational realities of shared vehicle systems with governmental carbon emission reduction policies and “double control” initiatives. Considering various perturbations, the paper constructs a Stackelberg short‐term model among diverse oligopolistic shared vehicle operators with technique sharing. It also develops a long‐term repeated game framework to scrutinize the impact of pertinent parameters on operators' decision variables and profits, along with system stability and complexity. The findings, elucidated through numerical analyses, reveal that the burgeoning sensitivity of users to energy conservation augments the overall shared vehicle market. The technique sharing mechanism boosts the benefit of the whole group of shared vehicle operators while diminishing the start‐up operators' revenue. In the long term, however, excessive price adjustments by SEV operators may lead to market chaos and profit erosion. Conversely, enhancing the adjustment coefficient of technological level levels by start‐up SEV2 operators may result solely in their own decision‐making becoming unmanageable. Finally, we found that both the methods of external force feedback control and parameter control are effective in restoring the chaotic market to stability.

CFI: a VR motor rehabilitation serious game design framework integrating rehabilitation function and game design principles with an upper limb case

Virtual reality (VR) Rehabilitation holds the potential to address the challenge that patients feel bored and give up long-term rehabilitation training. Despite the introduction of gaming elements by some researchers in rehabilitation training to enhance engagement, there remains a notable lack of in-depth research on VR rehabilitation serious game design methods, particularly the absence of a concrete design framework for VR rehabilitation serious games. Hence, we introduce the Clinical-Function-Interesting (CFI): a VR rehabilitation serious game design framework, harmonizing rehabilitation function and game design theories. The framework initiates with clinic information, defining game functions through the functional decomposition of rehabilitation training. Subsequently, it integrates gaming elements identified through the analysis and comparison of related literature to provide enduring support for long-term training. Furthermore, VR side-effect and enhancement are considered. Building upon this design framework, we have developed an upper limb VR rehabilitation serious game tailored for mild to moderate stroke patients and aligned our framework with another developed VR rehabilitation serious game to validate its practical feasibility. Overall, the proposed design framework offers a systematic VR rehabilitation serious game design methodology for the VR rehabilitation field, assisting developers in more accurately designing VR rehabilitation serious games that are tailored to specific rehabilitation goals.

An evolutionary differential game for regulating the role of monoclonal antibodies in treating signalling pathways in oesophageal cancer.

This work presents a new framework for a competitive evolutionary game between monoclonal antibodies and signalling pathways in oesophageal cancer. The framework is based on a novel dynamical model that takes into account the dynamic progression of signalling pathways, resistance mechanisms and monoclonal antibody therapies. This game involves a scenario in which signalling pathways and monoclonal antibodies are the players competing against each other, where monoclonal antibodies use Brentuximab and Pembrolizumab dosages as strategies to counter the evolutionary resistance strategy implemented by the signalling pathways. Their interactions are described by the dynamical model, which serves as the game's playground. The analysis and computation of two game-theoretic strategies, Stackelberg and Nash equilibria, are conducted within this framework to ascertain the most favourable outcome for the patient. By comparing Stackelberg equilibria with Nash equilibria, numerical experiments show that the Stackelberg equilibria are superior for treating signalling pathways and are critical for the success of monoclonal antibodies in improving oesophageal cancer patient outcomes.

Wage bargaining structure and political budget cycles: A policy game approach

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.

Interpreting the value of flexibility in AC security-constrained transmission expansion planning via a cooperative game framework

Security-constrained transmission expansion planning (SCTEP) is an inherently complex problem that requires simultaneously solving multiple contingency states of the system (usually corresponding to N-1 security criterion). Existing studies focus on effectively finding optimal solutions; however, single optimal solutions are not sufficient to interpret the value of flexibility (e.g., from energy storage systems) and support system planners in well-informed decision making. In view of planning uncertainties, it is necessary to estimate the contributions of flexibility to various objectives and prioritise the most effective investments. In this regard, this work introduces a SCTEP tool that enables interpreting the value of flexibility in terms of contributions to avoided load curtailment and total expected system cost reduction. Inspired by cooperative game theory, the tool ranks the contributions of flexibility providers and compares them against traditional line reinforcements. This information can be used by system planners to prioritise investments with higher contributions and synergistic capabilities.

Prospects of Interdisciplinary Research into the Problem of Resource Mobilization of Academic Staff

Introduction. Training students for innovative engineering activity is one of the priority tasks of an engineering university. However, so far all existing approaches to its solution involve changes in the curricula of degree programmes. The aim of the research is to substantiate and develop a methodological system of training future engineers in innovative engineering activity in the educational environment. Materials and Methods. The methodology of innovative engineering education, environmental, project, convergent and other approaches was used. A quantitative assessment of the level of development of innovative competencies was carried out during a comparative training experiment based on the average indicator of time series. The Pearson test was used to assess the statistical significance of the data. Results. The possibility of preparing future engineers for innovative engineering activities during a comprehensive course projecting in general engineering disciplines without departure from the curriculum is substantiated. To create conditions for such training, a project-based and activity-based educational environment has been proposed, pooling into one system all the resources available at the university and ensuring their interaction on the basis of a convergent approach associated with the approximation and interpenetration of scientific, pedagogical and information technology knowledge. A system for teaching innovative engineering activities in this environment has been developed, including conceptual-target, content, procedural-technological and reflective components, implemented within the framework of a business game. Discussion and Conclusion. The conclusions made by authors contribute to the development of the environment approach to learning in terms of designing new educational environments, theory and methodology of teaching technical disciplines, as well as project-based learning – in terms of their focus on innovative training of students.

Assessing the Effect of Traditional Games on Manipulative Movements in Elementary School Students Based on Gender

Background. Manipulative movements are essential for children’s development, which can be found in traditional games, representing manifestation of local wisdom that has been passed down from generation to generation. Objectives. This study aimed to examine the effect of traditional games on the manipulative movements of elementary school students based on gender. Materials and methods. This experimental study comprised two pretest-posttest groups without control variables. Data collection on pretest and posttest was carried out using three types of tests, namely throwing, catching, and kicking. A total of 60 students aged between 9 and 12 years were selected to participate in this study. The sample consisted of 30 male students (height 140.21±6.2 cm, and weight 35.77±5.6 kg), and 30 female students (height 138.4±6.8 cm and weight 34±4.1 kg). Results. The t-test analysis showed that the test results for male students were as follows: throwing 0.011<0.05, catching 0.007<0.05, and kicking 0.003<0.05. Then, the test results for the female students were: throwing 0.013<0.05, catching 0.017<0.05, and kicking 0.012<0.05. The results of the independent t-test indicated that the throwing, catching, and kicking tests revealed a statistical significance (p < 0.05) in both male and female students. Conclusions. The implementation of traditional games has been found to enhance the manipulative movements of elementary school students, as evidenced by positive changes observed in the pretest and posttest results. The improvement was achieved, among others, through the adaptation of traditional games following the characteristics of students’ development. Therefore, the conceptualization of physical learning within the framework of traditional games proved to be applicable and practical.

Effect of Private Deliberation: Deception of Large Language Models in Game Play.

Integrating large language model (LLM) agents within game theory demonstrates their ability to replicate human-like behaviors through strategic decision making. In this paper, we introduce an augmented LLM agent, called the private agent, which engages in private deliberation and employs deception in repeated games. Utilizing the partially observable stochastic game (POSG) framework and incorporating in-context learning (ICL) and chain-of-thought (CoT) prompting, we investigated the private agent's proficiency in both competitive and cooperative scenarios. Our empirical analysis demonstrated that the private agent consistently achieved higher long-term payoffs than its baseline counterpart and performed similarly or better in various game settings. However, we also found inherent deficiencies of LLMs in certain algorithmic capabilities crucial for high-quality decision making in games. These findings highlight the potential for enhancing LLM agents' performance in multi-player games using information-theoretic approaches of deception and communication with complex environments.

A Blockchain-Based Reliable Federated Meta-Learning for Metaverse: A Dual Game Framework

A Blockchain-Based Reliable Federated Meta-Learning for Metaverse: A Dual Game Framework

Modelling and Assessing the Advantages of Integrating Wind, Solar, and Coal Systems within an Annual Bilateral Trading Setting

The integration and co-location of new energy sources and thermal power generation within the same grid connection point, under the management of a single market operator, provide noteworthy potential for exploration in the northern part of our nation. This method is based on the premise of allocating new energy resources primarily for generating contracted electricity, while using thermal power to offer ancillary services. This strategy aims to integrate and use the distinct benefits of both thermal power and new energy sources. The yearly bilateral trade market has significant potential for growth and development. In order to model and evaluate the income generated by the interconnected system’s involvement in the yearly bilateral trading market, this study first establishes the definition of the interconnected system and examines its research significance in engaging in annual bilateral trading. This study utilizes the theoretical framework of master-slave games to analyze the involvement of a coupled system in yearly bilateral trade. The specific case examined in this research is a wind-solar-thermal coupling system located in a particular location of Liaoning Province. This study examines the economic advantages of engaging in the electricity market by considering the marginal cost and LCOE (Levelized Cost of Electricity) perspectives. The findings suggest a notable enhancement in the advantages of the integrated system inside the yearly bilateral trade market, in contrast to conventional power sources present in the market, as well as instances when these sources function autonomously without integration.

A game theory competitive intelligence solution stimulated from a Stackelberg game: A three players scenario

Competitive Intelligence (CI) involves systematically gathering information about the competitive landscape to anticipate rivals’ decisions and secure a strategic advantage. As academic interest in CI grows, the existing literature reflects a diverse body of knowledge. However, few works address the practical aspects of CI comprehensively, presenting viable solutions to its challenges. The motivation behind this paper is not only the scarcity of practical studies on CI but also the importance of CI and its benefits within companies, including improved decision-making and its positive impact on performance and sustainable growth. This study aims to contribute to the literature by proposing a CI solution grounded in game theory. We assert that applying game theory to CI is both intuitive and natural, given that the competitive environment readily lends itself to a game model. Viewing competitors as players, each striving to maximize profit, aligns seamlessly with game theory principles. We chose to consider a scenario with one initiator and multiple followers and model it as a Stackelberg game within the extensive form game framework. The literature review showed that the computational complexity of Stackelberg Equilibrium becomes NP-hard in most game classes with more than two players. This challenge encouraged us to contribute to the literature and focus on a scenario with two followers (three players), modeling the game in the extensive game form. To find a solution to this challenge, we used a modified version of the backward induction algorithm. To assess our solution’s efficacy, we conduct tests on 26 games (26 data instances), comparing results with those obtained using CPLEX and Decision Tree, and MiniMax methods. The ensuing pairwise sign test establishes the competitiveness of our outcomes. This research significantly contributes to the CI literature, offering a game theory-based solution and demonstrating its practical applicability through evaluation.

Impact of Capital Position and Financing Strategies on Encroachment in Supply Chain Dynamics

Channel encroachment and financing decisions are prevalent in practice. Utilizing the Stackelberg game framework, we investigate the impact of a retailer’s capital position and financing strategies on supply chain dynamics in which a supplier considers establishing a direct sales channel. We find that the retailer’s equilibrium financing strategy is impacted by demand volatility and the initial working capital. The supplier’s encroachment decision hinges on the entry cost when neither trade credit financing nor bank credit financing is available. When both types of credit are available, the choice of financing is a complex interplay involving initial working capital, entry cost, and demand volatility. Notably, the supplier’s decision to encroach may shift from a binary stance of either encroaching or not encroaching, or it may oscillate from encroachment to non-encroachment and back to encroachment, particularly with an increase in demand volatility when the entry cost is moderate. The novelty of this study lies in its integration of supplier channel decisions with retailer operational decisions and financing strategies, examining how the capital position and financing strategies impact channel decisions. This study provides managerial insights into the interplay between supplier’s channel dynamics and retailer’s financial considerations, shedding light on unexplored aspects of channel management. In future studies, some assumptions in this study can be modified to obtain more managerial insights.

Cournot Policy Model: Rethinking centralized training in multi-agent reinforcement learning

This work studies Centralized Training and Decentralized Execution (CTDE), which is a powerful mechanism to ease multi-agent reinforcement learning. Although the centralized evaluation ensures unbiased estimates of Q-value, peers with unknown policies make the decentralized policy far from the expectation. To make progress in more stabilized and effective joint policy, we develop a novel game framework, termed Cournot Policy Model, to enhance the CTDE-based multi-agent learning. Combining the game theory and reinforcement learning, we regard the joint decision-making in a single time step as a Cournot duopoly model, and then design a Hetero Variational Auto-Encoder to model the policies of peers in the decentralized execution. With a conditional policy, each agent is guided to a stable mixed-strategy equilibrium even though the joint policy evolves over time. We further demonstrate that such an equilibrium must exist in the case of centralized evaluation. We investigate the improvement of our method on existing centralized learning methods. The experimental results on a comprehensive collection of benchmarks indicate our approach consistently outperforms baseline methods.

Zero‐sum game‐based H∞ optimal finite‐time prescribed performance control for nonlinear multiagent systems with actuator faults

AbstractThis article proposes an optimal leader‐follower consensus control protocol with finite‐time prescribed performance for nonlinear multiagent systems suffering from the actuator fault based on the zero‐sum game framework. First, to guarantee the specified performance of the system within a finite time frame, a novel error transformation function (ETF) is constructed. The ETF proposed in this paper can adjust the mapping range of error transformation to achieve better error convergence performance, thereby enhancing the flexibility of the controller design. Then, to compensate for the negative impact of actuator fault, an error‐related item is separated from the optimal performance index function to design an online fault estimator, which can obtain a better error estimation accuracy. Furthermore, to lessen the need for difficult‐to‐verify persistent excitation signal in adaptive dynamic programming algorithm, both historical and real‐time data are applied to adjust the updating law of neural network weight. Moreover, it demonstrates that the signals within the closed‐loop system are bounded and the expected finite‐time prescribed performance can be ensured in the presence of faults. Finally, a numerical example of multiple single‐link robots manipulator system is executed to validate the efficacy of the developed scheme.