Cooperative Game Approach Research Articles

Optimizing integrated energy systems at park level: A cooperative game approach with exergy economics

This study presents a comprehensive framework for optimizing energy systems by integrating exergy analysis, energy economics, and game theory. The concept of exergy, which quantifies the usable energy within a system, is employed to evaluate energy efficiency and losses across various energy sources, including thermal, cooling, chemical, and electrical systems. Stoichiometric coefficients, denoted by the factor λ, are utilized to simplify exergy calculations for different energy types and processes. The economic evaluation of energy flows is conducted through energy economics principles, incorporating cost allocation and balance equations. The integration of game theory into the optimization model ensures strategic interactions among energy components, leading to a Nash equilibrium that balances economic performance, efficiency, and environmental sustainability. The model also accounts for emissions and the required proportion of renewable energy. To solve the complex optimization problem, a modified Particle Swarm Optimization (PSO) algorithm is employed, featuring adaptive mechanisms for velocity and inertia updates, enhancing the search process for the optimal solution. The proposed framework is designed to optimize the Integrated Energy System (IES) efficiently, ensuring sustainable and economically viable energy management. The analysis of optimization strategies highlights a trade-off between cost and efficiency. Strategy 1, focused on minimizing cost, achieves the lowest cost at 4069.37 CNY, 25.79 % less than Strategy 2, but with a reduced exergy efficiency of 59.82 %, which is 10.14 % lower than Strategy 2′s 68.47 %. Strategy 3 offers a balanced approach, with a cost of 4970.89 CNY, 9.43 % higher than Strategy 1 but 9.43 % lower than Strategy 2. It achieves an exergy efficiency of 67.87 %, only 0.60 % lower than Strategy 2, thus providing a practical compromise between economic performance and efficiency.

A Cooperative Game Approach for Optimal Design of Shared Energy Storage System

The energy sector’s long-term sustainability increasingly relies on widespread renewable energy generation. Shared energy storage embodies sharing economy principles within the storage industry. This approach allows storage facilities to monetize unused capacity by offering it to users, generating additional revenue for providers, and supporting renewable energy prosumers’ growth. However, high investment costs and long payback periods often hinder the development of battery storage. To address this challenge, we propose a shared storage investment framework. In this framework, a storage investor virtualizes physical storage equipment, enabling prosumers to access storage services as though they owned the batteries themselves. We adopt a cooperative game approach to incorporate storage sharing into the design phase of energy systems. To ensure a fair distribution of cooperative benefits, we introduce a benefit allocation mechanism based on contributions to energy storage sharing. Utilizing realistic data from three buildings, our simulations demonstrate that the shared storage mechanism creates a win–win situation for all participants. It also enhances the self-sufficiency and self-consumption of renewable energy. This paper provides valuable insights for shared storage investors regarding optimal design and benefit allocation among multiple stakeholders.

Game on for Climate Action: Big Game Delivers Engaging STEM Learning

A decline in European students’ interest in STEM subjects, exacerbated by the COVID-19 pandemic’s disruption of education, has raised concerns about the continent’s future workforce. To address this challenge, this study investigates the efficacy of the BIG GAME project methodology, a cooperative story-driven digital game approach designed to engage secondary students in collaborative environmental problem-solving. Implemented across Romania, Italy, Estonia, and Finland, this six-month study employed a mixed-methods design involving 62 teachers and 239 students in ten distinct game missions focused on environmental challenges. The quantitative results indicated significant improvements in students’ transversal skills (teamwork, communication, and critical thinking), as reported by over 75% of teachers. The qualitative data emphasised the value of structured peer review in developing students’ reflective practices. This research underscores the importance of teacher facilitation in game-based learning and problem-based simulations and highlights the potential of such methodologies to boost student engagement and environmental awareness. These findings suggest that the BIG GAME project approach could be a valuable tool for revitalising STEM education and cultivating future-ready citizens.

Optimal resource allocation in hierarchical organizations under uncertainty: An interval-valued n-person cooperative game approach

In many real production scenarios, departmental organizations often exhibit a hierarchical structure, where departments cooperate with subordinate departments to optimize resource allocation and maximize their respective benefits. However, due to a lack of information or data, many model parameters in the allocation process cannot be precisely defined. In response to this challenge, an interval n-person hierarchical resource allocation model is proposed to achieve maximum economic benefit in uncertain environments. Based on the concepts of satisfactory degrees of comparing intervals and interval-valued cores of interval-valued n-person cooperative games, an auxiliary nonlinear programming model and method are developed to solve the interval-valued cores of such cooperative games. The approach explicitly considers the inclusion and/or overlap relations between intervals, whereas the traditional interval ranking method may not guarantee the existence of interval-valued cores. The proposed method offers cooperative opportunities under uncertain conditions. Finally, the feasibility and applicability of the models and methods are demonstrated through a numerical example and comparison with other methods.

Risk sharing rule and safety loading in a peer to peer cooperative insurance model

AbstractThe evolution of digital technologies is reshaping consumer habits and needs, driving process automation, and giving rise to innovative business models like Insurtech. Peer-to-peer (P2P) insurance is emerging as part of this trend. P2P involves purchasing an insurance policy by sharing the risk with a group of peers. This group transparently monitors real-time savings and tracks claims filed by its members. At the policy’s expiration, if the actual risk is lower than anticipated, the peers receive a partial refund of their premium. This paper introduces a model to determine the entry price in a broker-based P2P scheme using a cooperative game approach. We employ the Shapley Value method to distribute the risk among participants. Numerical examples are included for illustration and discussion.

Improving Salt Farmer’s Bargain Power through Demand Allocation and Profit Sharing: A Cooperative Game Approach

Improving Salt Farmer’s Bargain Power through Demand Allocation and Profit Sharing: A Cooperative Game Approach

Cooperation for trans-regional electricity trading from the perspective of carbon quota: A cooperative game approach

Trans-regional electricity trading is a meaningful way to optimize resource allocation and achieve carbon peak and carbon neutrality goals. In this paper, we construct the trans-regional electricity trading cooperative game models considering the impact of local microgrid integration. Based on the cooperative game theory with coalition and graph structures, the optimal mode of trans-regional electricity cooperation and the impact of different carbon quota systems on cooperation profits are studied. The profits obtained through the trans-regional electricity trading are reasonably distributed by the profit distribution scheme based on the Owen graph value. The theoretical and numerical simulation results demonstrate that the local microgrid and the bulk power grid form a priori union, and then participate in the trans-regional electricity trading can obtain more profits. In addition, when the low-carbon policy on the demand side of electricity becomes more relaxed, the implementation of a carbon quota shared responsibility between producers and consumers will be more effective than producer responsibility. Compared with the Myerson value, the profit distribution scheme based on the Owen graph value is more suitable for distributing the profits obtained through trans-regional electricity trading.

Stable streaming platforms: a cooperative game approach

Streaming platforms such as Spotify are popular media services where content creators may offer their content. Because these platforms operate in a highly competitive market, content creators may leave the platform and join elsewhere. This paper studies conditions under which content creators have no incentives to leave the platform and thus stability can be preserved. We introduce a stylized model for streaming platform situations and associate these situations with a cooperative game. We focus on the (non)emptiness of the core to analyze the stability of the streaming platforms. It turns out that both stable and unstable streaming platforms exist. We show that for streaming platforms operating in a market where users have completely opposite streaming behavior, stability cannot always be preserved. However, in markets where users are more similar in their streaming behavior, stability can be preserved. We further analyze the stability of streaming platforms by means of numerical experiments. Our results indicate that stability of streaming platforms generally is a delicate matter. Streaming platforms are more likely to be stable in markets where users are similar in their streaming behavior. To avoid that content creators leave the platform, it is therefore recommended to focus on particular market segments where these similarities occur.

Remote Parkinson's disease severity prediction based on causal game feature selection

Telemonitoring of Parkinson's disease has important implications for early diagnosis and treatment of patients. Most of the existing feature selection methods for remote prediction of PD severity are based on correlation and rarely consider causality, thus compromising the robustness of the model. Therefore, a causal game-based feature selection (CGFS) model is proposed for remote PD symptom severity assessment. Firstly, to address the challenge of small data size, the similar patient transfer strategy is designed to find data from source domain patients with conditions similar to those of the target patient. Secondly, the undirected equivalent greedy search method is employed to construct the causal graph between features and PD severity scores, and the robustness of the model is improved by selecting causal features. Then, to enhance the prediction accuracy, this paper utilizes the cooperative game approach Shapley value to evaluate the contribution of neighborhood nodes of the target value, and selects the features with causality and high contribution to form the final feature subset. Finally, the subset is input into the random forest to further enhance robustness and performance of the model. Experiments on Parkinson’s telemonitoring dataset and the tapping dataset with different biomarkers show that the robustness of the feature subset selected by the CGFS model, and the prediction performance is better than advanced models compared. Therefore, the validity and universality of the CGFS method is demonstrated in remote PD severity prediction.

A Cooperative Game Approach to Integrated Healthcare

Cet article examine le partage d’un forfait de soins dans le cadre d’un système au parcours de soins. Nous modélisons ce problème par l’intermédiaire des outils de la théorie des jeux. Différentes approches sont envisagées, chacune donnant lieu à un jeu coopératif particulier, et permettant de prendre en compte la chronologie des soins. La valeur de Shapley, une règle d’allocation prioritaire et une règle d’allocation proportionnelle sont utilisées pour rembourser (partiellement) les professionnels de santé sur la base du forfait payé par le patient. Des propriétés de ces différentes règles d’allocation sont établies. Nous montrons également que le cœur de certains de ces jeux coopératifs est non-vide et peut contenir ces règles d’allocation. JEL codes : C71, I10

Participation of strategic district heating networks in electricity markets: An arbitrage mechanism and its equilibrium analysis

Combined electricity-heat operation improves social welfare compared with the traditional heat-driven operation. However, it is left open how to achieve such an improvement in the current electricity market. Therefore, an arbitrage mechanism enabling strategic district heating networks (DHNs) to participate in electricity markets is designed, which settles the payment concerning the power deviation and the locational marginal price (LMP). Individual interests of both energy sectors are addressed via a bi-level model, while analytical results of the arbitrage equilibrium are proved theoretically. Although the mechanism intends to allow DHNs to profit selfishly from utilizing energy storage, it is strikingly guaranteed that electric power networks also benefit from this. A Pareto improvement is thus achieved by the mechanism with enhanced social welfare efficiency at the arbitrage equilibrium. The proposed mechanism is numerically compared with the traditional heat-driven operation, combined operation and existing cooperative and non-cooperative game approaches, while the merits are verified in two integrated electricity and heat systems with different scales.

Day‐ahead operation strategy for multiple data centre prosumers: A cooperative game approach

AbstractThe transferrable characteristics of workloads both spatial and temporal have received much attention recently. A data centre prosumer (DCP) is created by combining multiple data centre buildings, which contain workloads, photovoltaic generations, and battery energy storage systems (BESSs). Few studies have considered electricity trading and payoff sharing among various DCPs in a data centre park. This paper presents a cooperative framework for interconnected DCPs in a data centre park and proposes a novel day‐ahead operation strategy considering uncertainties in photovoltaic (PV) generations and workloads using the equivalent linear robust reformation method. The operation strategy is formulated as an asymmetric Nash bargaining cooperative game, which aims at maximizing the overall payoff of the cooperative alliance while considering the contributions of shared electricity to share the payoff. To solve the formulated cooperative game problem while preserving user privacy, an enhanced self‐adaptive prediction‐correction‐based alternating direction multiplier method (PCB‐ADMM) algorithm with adaptive penalty coefficients to accelerate convergence is employed in a distributed manner. The case studies indicate a 6.63% reduction in overall cost and verify the feasibility and fairness of the proposed cooperative strategy. The enhanced self‐adaptive PCB‐ADMM algorithm also shows superiority over other ADMM algorithms in effectiveness and rationality.

Workload Re-Allocation for Edge Computing With Server Collaboration: A Cooperative Queueing Game Approach

In this paper, a long-term workload management problem for multi-server edge computing with server collaboration is studied. In the considered model, mobile users computation-intensive tasks are generated dynamically over the time and offloaded to associated edge servers according to pre-determined subscription agreements. Upon receiving the subscribed workload, each edge server can then decide to whether participate in server collaboration for enabling workload re-allocation (i.e., workload exchange) with other heterogeneously configured edge servers. Unlike most of the existing work, this paper takes into account both competitions and collaborations among strategic edge servers in sharing their computing capacities. To achieve the equilibrium for each edge server in minimizing its expected cost (including energy consumption, delay, transmission, configuration and pricing costs), a joint optimization is formulated for determining i) its amount of workload to undertake, ii) compensation price charged from peers, and iii) computing speed to adopt. To efficiently solve this problem, we propose a novel cooperative queueing game approach, which integrates a convex optimization, a core cost sharing scheme and a mapping rule. Theoretical analyses and extensive simulations are conducted to evaluate the performance of the proposed solution, and demonstrate its superiority over counterparts.

A cooperative game approach to synthesizing a sequential distributed model predictive controller

A cooperative game approach to synthesizing a sequential distributed model predictive controller

Coordination of two competing closed-loop supply chains: A cooperative game approach

In the development of end-of-life (EOL) products recycling, coordinating competing closed-loop supply chains (CLSCs) with restricted coalition has become an important topic that has yet to be thoroughly investigated. In this study, we first investigate the possible coalitions for two CLSCs composed of manufacturers and third-party recyclers under a restricted coalition structure, which is used for deriving the characteristic functions representing the bargaining powers of different coalitions and allocating the overall profits. Subsequently, to fairly allocate the maximal profit, we establish a cooperative game in the form of characteristic function for the two CLSCs and use an advanced solution concept (average tree value) to coordinate them. We find that: compared to other non-cooperative and partial cooperative models, the centralized model can always achieve the best performance, e.g., the highest recovery rate. And the profit of the fully centralized model increases linearly with the increase of the cooperation coefficient. When the third-party recyclers of two CLSCs form alliance, the profit of the manufacturer is positively or negatively correlated with the cooperation coefficient due to the difference of the model and price elasticity coefficient. Under the cooperation of two CLSCs third-party recyclers, the relationship between the profit of the third-party recycler, the profit of the single chain system or the profit of the double chain system and the cooperation coefficient increases first and then decreases, but the inflection point is different. The coordination of two competing CLSCs can be well addressed by the allocation scheme proposed in this study, while satisfying the collective and individual rationalities.

Collaborative Coded Distributed Computing Scheme: A Two-Phase Cooperative Game Approach

As a modern communication paradigm, Artificial intelligence based Internet of Things (AIoT) can provide an interactive platform across the globe to enrich the quality of networking services. With the AIoT paradigm, coded distributed computing (CDC) has recently emerged to be a promising solution to address the straggling effects in conventional distributed computing systems. In this article, we propose a novel CDC control scheme in the AIoT platform. Based on the cooperative game theory, the main challenges of our scheme are i) the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> value decision for the CDC process, and ii) edge node resource allocation for offloading tasks. Using the ideas of coalition game and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">weighted Nash social welfare solution (WNSWS)</i> , our proposed scheme is developed as a two-phase game model to achieve a mutually desirable solution. At the first phase, a dynamic coalition formation is proceeded to select the most adaptable edge nodes for the offloading subtasks. At the second phase, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WNSWS</i> is adopted to effectively share each edge node’s computing resource. Based on the jointly design of these two cooperative games, we explore the synergy effect to optimize the CDC process. In the edge assisted distributed computing infrastructure, our reciprocal combinative approach can provide a fair-efficient solution through the sequential interactions of edge nodes and AIoT devices. In the performance evaluation, we provide extensive simulation analyses to show our scheme’s superiority by comparing with the existing baseline protocols.

Capacity Allocation of Hybrid Power System with Hot Dry Rock Geothermal Energy, Thermal Storage, and PV Based on Game Approaches

This study utilizes hot dry rock (HDR) geothermal energy, which is not affected by climate, to address the capacity allocation of photovoltaic (PV) -storage hybrid power systems (HPSs) in frigid plateau regions. The study replaces the conventional electrochemical energy storage system with a stable HDR plant assisted by a flexible thermal storage (TS) plant. An HPS consisting of an HDR plant, a TS plant, and a PV plant is proposed. Game approaches are introduced to establish the game pattern model of the proposed HPS as the players. The annualized income of each player is used as the payoff function. Furthermore, non-cooperative game and cooperative game approaches for capacity allocation are proposed according to the interests of each player in the proposed HPS. Finally, the proposed model and approaches are validated by performing calculations for an HPS in the Gonghe Basin, Qinghai, China as a case study. The results show that in the proposed non-cooperative game approach, the players focus only on the individual payoff and neglect the overall system optimality. The proposed cooperative game approach for capacity allocation improves the flexibility of the HPS as well as the payoff of each game player. Thereby, the HPS can better satisfy the power fluctuation rate requirements of the grid and increase the equivalent firm capacity (EFC) of PV plants, which in turn indirectly guarantees the reliability of grid operation.

A cooperative game approach for optimal resiliency-oriented scheduling of transactive multiple microgrids

The growth of distributed energy resources and microgrids (MGs) attracts attention to the transactive multiple MG (TMMG) concept. This paper proposes a novel framework that belongs to the competitive-based resilient scheduling of TMMGs. A cooperative game approach is investigated for optimal day-ahead scheduling of TMMGs, which concerns the possibility of long-duration disconnection from the main grid. The TMMG comprises multiple MGs that can have energy transactions through a local market. This local energy market lets the TMMG operator receive the MGs' 24-hour bid-offer amounts and set the hourly transaction prices. The proposed game fulfills the minimum operation cost for MGs in the normal operation mode (NOM) and ensures the serving of TMMG's load during the resiliency operation mode (ROM). Thus, the paper seeks to find an equilibrium point so that all the MGs reach acceptable strategies by meeting the constraints in the NOM and ROM. It is shown that the market tends to provide the NOM transaction at clearing prices lower than the wholesale price. Also, it tends to disperse a higher price in the ROM condition. Notwithstanding the profitable opportunity for renewable-penetrated MGs, they are exposed to high costs due to the inherent uncertainty and risk of generation deficiency.

A cooperative game approach for energy management of interconnected microgrids

• A cooperative game approach for energy scheduling of multi-microgrid systems. • Applying shapley value to fairly allocate multi-microgrid system cost between microgrids. • Considering the uncertainties related to the demand, renewable outputs, and market prices. • Enhancing the flexibility of the multi-microgrid system by energy transactions of microgrids. • Deliberating a price-based demand response to facilitate the cost-saving of microgrids. This paper proposes a cooperative game to schedule the day-ahead operation of multi-microgrid (MMG) systems. In the proposed model, microgrids are scheduled to achieve a global optimum for the cost of the multi-microgrid system. The minimum cost is achieved by transactions of microgrids with each other. Also, price-based demand response is implemented in the model to build a cost-reducing opportunity for consumers. Applying Shapley value, the optimum cost of the MMG system is fairly allocated between microgrids. To enhance the confidence level of results, data uncertainties are incorporated into the model. The uncertainties of renewable outputs, demand, and prices of trading with the main grid are applied into the model. The presented model is developed as a mixed-integer nonlinear programming problem, and its efficiency is evaluated on a standard test system containing three microgrids. The cost of the MMG system when microgrids form a cooperative game is compared with the isolated status that microgrids do not transact energy with each other. The results indicate that the cost of the MMG is declined using the proposed cooperative model in comparison with the isolated mode. Also, the cost of microgrid1, microgrid2, and microgrid3 are improved by 2.4, 2.7, and 11.8%, respectively.

TSO-DSOs Stable Cost Allocation for the Joint Procurement of Flexibility: A Cooperative Game Approach

In this paper, a transmission-distribution systems flexibility market is introduced, in which system operators (SOs) jointly procure flexibility from different systems to meet their needs (balancing and congestion management) using a common market. This common market is, then, formulated as a cooperative game aiming at identifying a stable and efficient split of costs of the jointly procured flexibility among the participating SOs to incentivize their cooperation. The non-emptiness of the core of this game is then mathematically proven, implying the stability of the game and the naturally-arising incentive for cooperation among the SOs. Several cost allocation mechanisms are then introduced, while characterizing their mathematical properties. A case study is then presented, considering an interconnected system composed of the IEEE 14-bus transmission system and the Matpower 18-bus, 69-bus, and 141-bus distributions systems. The numerical results showcase the cooperation-induced reduction in system-wide flexibility procurement costs, and identify the varying costs borne by the different SOs under different cost allocations methods.