{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T15:55:15Z","timestamp":1778082915074,"version":"3.51.4"},"reference-count":140,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2023,12,17]],"date-time":"2023-12-17T00:00:00Z","timestamp":1702771200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Portuguese Foundation for Science and Technology (FCT)","award":["2020.07048.BD"],"award-info":[{"award-number":["2020.07048.BD"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>The role of prosumers is changing as they become active and empowered members of the grid by exchanging energy. This introduces bidirectional power flow and other challenges into the existing power systems, which require new approaches capable of dealing with the increased decentralization and complexity. Such approaches rely on game-theoretic models and mechanisms to analyze strategic decisions in competitive settings. More specifically, a coalitional game can encourage participants to trade energy with one another and obtain fair and sustainable outcomes. Therefore, the contents of this work address the coalitional game for sustainable energy trading, as well as the challenges associated with its application in power systems. This is achieved by identifying literature works that successfully implemented coalitional games in energy trading and management applications while providing an overview of solution concepts and discussing their properties and contributions to sustainability. Moreover, this work also proposes conditions that peer-to-peer energy trading should satisfy to be considered sustainable. Finally, a case study is presented to demonstrate how a coalitional game and various solution concepts can be successfully implemented to ensure the benefits and stability of cooperation in power systems. The weighted Shapley value is proposed to allocate profits among communities according to their level of sustainability.<\/jats:p>","DOI":"10.3390\/en16248115","type":"journal-article","created":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T11:28:07Z","timestamp":1702898887000},"page":"8115","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Application and Challenges of Coalitional Game Theory in Power Systems for Sustainable Energy Trading Communities"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0801-7432","authenticated-orcid":false,"given":"Filipe","family":"Bandeiras","sequence":"first","affiliation":[{"name":"Smart Cities Research Center (Ci2-IPT), 2300-313 Tomar, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1229-6243","authenticated-orcid":false,"given":"\u00c1lvaro","family":"Gomes","sequence":"additional","affiliation":[{"name":"Institute for Systems Engineering and Computers at Coimbra (INESC Coimbra), 3030-290 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0120-8247","authenticated-orcid":false,"given":"M\u00e1rio","family":"Gomes","sequence":"additional","affiliation":[{"name":"Smart Cities Research Center (Ci2-IPT), 2300-313 Tomar, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7632-0690","authenticated-orcid":false,"given":"Paulo","family":"Coelho","sequence":"additional","affiliation":[{"name":"Smart Cities Research Center (Ci2-IPT), 2300-313 Tomar, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.rser.2016.06.008","article-title":"Managing electric flexibility from Distributed Energy Resources: A review of incentives for market design","volume":"64","author":"Eid","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.enpol.2013.06.108","article-title":"The influence of distributed generation penetration levels on energy markets","volume":"62","author":"Vahl","year":"2013","journal-title":"Energy Policy"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhu, J. (2015). Optimization of Power System Operation, Wiley-IEEE Press. [2nd ed.].","DOI":"10.1002\/9781118887004"},{"key":"ref_4","unstructured":"(2023, October 20). World Cities Report 2020: The Value of Sustainable Urbanization. United Nations Human Settlements Programme (UN-Habitat). Available online: https:\/\/unhabitat.org\/sites\/default\/files\/2020\/10\/wcr_2020_report.pdf."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Leal Filho, W., Azul, A., Brandli, L., \u00d6zuyar, P., and Wall, T. (2020). Affordable and Clean Energy. Encyclopedia of the UN Sustainable Development Goals, Springer.","DOI":"10.1007\/978-3-319-71057-0"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apenergy.2018.03.010","article-title":"Peer-to-Peer energy trading in a Microgrid","volume":"220","author":"Zhang","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"118400","DOI":"10.1016\/j.apenergy.2021.118400","article-title":"A peer-to-peer energy trading market embedded with residential shared energy storage units","volume":"308","author":"Zheng","year":"2022","journal-title":"Appl. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bandeiras, F., Gomes, \u00c1., Gomes, M., and Coelho, P. (2023). Exploring Energy Trading Markets in Smart Grid and Microgrid Systems and Their Implications for Sustainability in Smart Cities. Energies, 16.","DOI":"10.3390\/en16020801"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"111056","DOI":"10.1016\/j.rser.2021.111056","article-title":"Review of Cooperative Game Theory applications in power system expansion planning","volume":"145","author":"Churkin","year":"2021","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1109\/MSP.2009.000000","article-title":"Coalitional game theory for communication networks","volume":"26","author":"Saad","year":"2009","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MSP.2018.2818327","article-title":"Transforming Energy Networks via Peer-to-Peer Energy Trading: The potential of game-theoretic approaches","volume":"35","author":"Tushar","year":"2018","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Gautam, M., and Ben-Idris, M. (2023, January 13\u201314). Coalitional Game Theory in Power Systems: Applications, Challenges, and Future Directions, Systems and Control. Proceedings of the 2023 IEEE Texas Power and Energy Conference (TPEC), College Station, TX, USA.","DOI":"10.1109\/TPEC56611.2023.10078455"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Navon, A., Ben Yosef, G., Machlev, R., Shapira, S., Roy Chowdhury, N., Belikov, J., Orda, A., and Levron, Y. (2020). Applications of Game Theory to Design and Operation of Modern Power Systems: A Comprehensive Review. Energies, 13.","DOI":"10.3390\/en13153982"},{"key":"ref_14","unstructured":"(2023, November 30). Orchestrating Infrastructure for Sustainable Smart Cities, International Electrotechnical Commission (IEC). Available online: https:\/\/www.iec.ch\/basecamp\/orchestrating-infrastructure-sustainable-smart-cities."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"77","DOI":"10.3389\/fbuil.2020.00077","article-title":"The Concept of Sustainability in Smart City Definitions","volume":"6","author":"Maria","year":"2020","journal-title":"Front. Built Environ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1023\/A:1006697118620","article-title":"Economic, social, and environmental sustainability in development theory and urban planning practice","volume":"19","author":"Basiago","year":"1998","journal-title":"Environmentalist"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"110311","DOI":"10.1016\/j.rser.2020.110311","article-title":"Review of the cooperation and operation of microgrid clusters","volume":"133","author":"Bandeiras","year":"2020","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"134","DOI":"10.3389\/fenrg.2022.810395","article-title":"Recent Trends, Challenges, and Future Aspects of P2P Energy Trading Platforms in Electrical-Based Networks Considering Blockchain Technology: A Roadmap Toward Environmental Sustainability","volume":"10","author":"Javed","year":"2022","journal-title":"Front. Energy Res."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gilles, R.P. (2010). The Cooperative Game Theory of Networks and Hierarchies, Springer. Theory and Decision Library C, 44.","DOI":"10.1007\/978-3-642-05282-8"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1000240","DOI":"10.4172\/2169-0316.1000240","article-title":"Using Game Theory to Develop Sustainability Strategies in an Era of Resource Depletion","volume":"7","author":"Seifi","year":"2018","journal-title":"Ind. Eng. Manag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"10134","DOI":"10.1073\/pnas.1208087109","article-title":"Extortion and cooperation in the Prisoner\u2019s Dilemma","volume":"109","author":"Stewart","year":"2012","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2662","DOI":"10.1109\/TPWRS.2014.2312021","article-title":"Multi-Regional Transmission Planning as a Non-Cooperative Decision-Making","volume":"29","author":"Tohidi","year":"2014","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.apenergy.2019.03.111","article-title":"A motivational game-theoretic approach for peer-to-peer energy trading in the smart grid","volume":"243","author":"Tushar","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Tushar, W., Yuen, C., Smith, D.B., Hassan, N.U., and Poor, H.V. (2015, January 3\u20136). A canonical coalitional game theoretic approach for energy management for nanogrids. Proceedings of the 2015 IEEE Innovative Smart Grid Technologies\u2014Asia (ISGT ASIA), Bangkok, Thailand.","DOI":"10.1109\/ISGT-Asia.2015.7387081"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Du, Y., Li, F., Kou, X., and Pei, W. (2017, January 16\u201320). Coordinating multi-microgrid operation within distribution system: A cooperative game approach. Proceedings of the 2017 IEEE Power & Energy Society General Meeting, Chicago, IL, USA.","DOI":"10.1109\/PESGM.2017.8273876"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1960","DOI":"10.1109\/TSG.2017.2784902","article-title":"Coalitional Game-Based Cost Optimization of Energy Portfolio in Smart Grid Communities","volume":"10","author":"Koivunen","year":"2019","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_27","first-page":"161","article-title":"Cooperation model in the electricity energy market using bi-level optimization and Shapley value","volume":"5","author":"Arboleda","year":"2018","journal-title":"Oper. Res. Perspect."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4379","DOI":"10.1109\/TSG.2018.2858206","article-title":"Sharing Storage in a Smart Grid: A Coalitional Game Approach","volume":"10","author":"Chakraborty","year":"2019","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"78266","DOI":"10.1109\/ACCESS.2021.3081871","article-title":"Coalitional Game Theory Based Value Sharing in Energy Communities","volume":"9","author":"Safdarian","year":"2021","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1109\/TPWRS.2018.2858540","article-title":"Incentivizing Prosumer Coalitions with Energy Management Using Cooperative Game Theory","volume":"34","author":"Han","year":"2019","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1109\/TPWRS.2018.2877236","article-title":"Real-Time Rolling Horizon Energy Management for the Energy-Hub-Coordinated Prosumer Community from a Cooperative Perspective","volume":"34","author":"Ma","year":"2019","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1729","DOI":"10.1109\/TPWRS.2019.2957537","article-title":"Coalitional Game-Based Transactive Energy Management in Local Energy Communities","volume":"35","author":"Feng","year":"2020","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.apenergy.2019.01.208","article-title":"Coalitional game theory based local power exchange algorithm for networked microgrids","volume":"239","author":"Mei","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1186\/s41601-019-0141-5","article-title":"Optimization of energy exchange in microgrid networks: A coalition formation approach","volume":"4","author":"Essayeh","year":"2019","journal-title":"Prot. Control. Mod. Power Syst."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Saad, W., Han, Z., and Poor, H.V. (2011, January 5\u20139). Coalitional Game Theory for Cooperative Micro-Grid Distribution Networks. Proceedings of the 2011 IEEE International Conference on Communications Workshops (ICC), Kyoto, Japan.","DOI":"10.1109\/iccw.2011.5963577"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"114436","DOI":"10.1016\/j.apenergy.2019.114436","article-title":"A coalition formation game framework for peer-to-peer energy trading","volume":"261","author":"Tushar","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Malik, S., Duffy, M., Thakur, S., and Breslin, J.G. (July, January 28). Fractional Hedonic Coalition Formation Game for Peer to Peer Energy Trading in a Microgrid. Proceedings of the 2021 IEEE Madrid PowerTech, Madrid, Spain.","DOI":"10.1109\/PowerTech46648.2021.9494877"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"107642","DOI":"10.1016\/j.ijepes.2021.107642","article-title":"A strategy-based coalition formation model for hybrid wind\/PV\/FC\/MT\/DG\/battery multi-microgrid systems considering demand response programs","volume":"136","author":"Karimi","year":"2022","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"e2313","DOI":"10.1002\/etep.2313","article-title":"Distributed generation for economic benefit maximization through coalition formation\u2013based game theory concept","volume":"27","author":"Marzband","year":"2017","journal-title":"Int. Trans. Electr. Energy Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1049\/iet-gtd.2014.1084","article-title":"Economic power transaction using coalitional game strategy in micro-grids","volume":"10","author":"Ni","year":"2016","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"108492","DOI":"10.1016\/j.ijepes.2022.108492","article-title":"Optimal coalition formation and maximum profit allocation for distributed energy resources in smart grids based on cooperative game theory","volume":"144","author":"Moafi","year":"2023","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"120221","DOI":"10.1016\/j.apenergy.2022.120221","article-title":"A communication-efficient coalition graph game-based framework for electricity and carbon trading in networked energy hubs","volume":"329","author":"Zhong","year":"2023","journal-title":"Appl. Energy"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4389","DOI":"10.1109\/TSG.2021.3070160","article-title":"Coalition Graph Game-Based P2P Energy Trading with Local Voltage Management","volume":"12","author":"Azim","year":"2021","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5585","DOI":"10.1109\/ACCESS.2020.3048329","article-title":"Profit-Sharing Rule for Networked Microgrids Based on Myerson Value in Cooperative Game","volume":"9","author":"Suh","year":"2021","journal-title":"IEEE Access"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1049\/iet-stg.2019.0171","article-title":"Multi-objective design method for construction of multi-microgrid systems in active distribution networks","volume":"3","author":"Moghateli","year":"2020","journal-title":"IET Smart Grid"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2263","DOI":"10.1109\/TSG.2015.2399497","article-title":"A Multiobjective Approach to Multimicrogrid System Design","volume":"6","author":"Chiu","year":"2015","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"106204","DOI":"10.1016\/j.ijepes.2020.106204","article-title":"Game-based peer-to-peer energy sharing management for a community of energy buildings","volume":"123","author":"Cui","year":"2020","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1109\/TFUZZ.2022.3220964","article-title":"Electric Vehicles Charging Dispatch and Optimal Bidding for Frequency Regulation Based on Intuitionistic Fuzzy Decision Making","volume":"31","author":"Li","year":"2023","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"6087","DOI":"10.1109\/TIE.2018.2874578","article-title":"Peer-to-Peer Energy Trading in a Prosumer-Based Community Microgrid: A Game-Theoretic Model","volume":"66","author":"Paudel","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1109\/JSAC.2013.130706","article-title":"Bidirectional Energy Trading and Residential Load Scheduling with Electric Vehicles in the Smart Grid","volume":"31","author":"Kim","year":"2013","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1016\/j.egyr.2022.10.168","article-title":"Energy trading management based on Stackelberg game theory to increase independence of microgrids","volume":"8","author":"Zheng","year":"2022","journal-title":"Energy Rep."},{"key":"ref_52","first-page":"505","article-title":"Transactive Energy and Flexibility Provision in Multi-microgrids Using Stackelberg Game","volume":"9","author":"Hua","year":"2023","journal-title":"CSEE J. Power Energy Syst."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"118944","DOI":"10.1016\/j.apenergy.2022.118944","article-title":"A Stackelberg game approach for energy sharing management of a microgrid providing flexibility to entities","volume":"316","author":"Erol","year":"2022","journal-title":"Appl. Energy"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"107865","DOI":"10.1016\/j.ijepes.2021.107865","article-title":"A priority-based approach for peer-to-peer energy trading using cooperative game theory in local energy community","volume":"137","author":"Malik","year":"2022","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_55","unstructured":"Osborne, M.J. (2000). An Introduction to Game Theory, Department of Economics, University of Toronto."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Huang, H., Nie, S., Lin, J., Wang, Y., and Dong, J. (2020). Optimization of Peer-to-Peer Power Trading in a Microgrid with Distributed PV and Battery Energy Storage Systems. Sustainability, 12.","DOI":"10.3390\/su12030923"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"100720","DOI":"10.1016\/j.segan.2022.100720","article-title":"Coalitional game theory approach for multi-microgrid energy systems considering service charge and power losses","volume":"31","author":"Modarresi","year":"2022","journal-title":"Sustain. Energy Grids Netw."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1109\/MSP.2012.2186410","article-title":"Game-Theoretic Methods for the Smart Grid: An Overview of Microgrid Systems, Demand-Side Management, and Smart Grid Communications","volume":"29","author":"Saad","year":"2012","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1016\/j.ejor.2014.10.037","article-title":"Common mistakes in computing the nucleolus","volume":"241","author":"Guajardo","year":"2015","journal-title":"Eur. J. Oper. Res."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"3185","DOI":"10.1109\/TSG.2020.2969657","article-title":"Peer-to-Peer Trading in Electricity Networks: An Overview","volume":"11","author":"Tushar","year":"2020","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"2615","DOI":"10.1049\/rpg2.12205","article-title":"A two-stage multi microgrids p2p energy trading with motivational game-theory: A case study in malaysia","volume":"15","author":"Yap","year":"2021","journal-title":"IET Renew. Power Gener."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01753431","article-title":"Cores of Convex Games","volume":"1","author":"Shapley","year":"1971","journal-title":"Int. J. Game Theory"},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Tucker, A.W., and Luce, R.D. (1959). Contributions to the Theory of Games IV, Princeton University Press. Annals of Mathematics Studies, 40.","DOI":"10.1515\/9781400882168"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Moncecchi, M., Meneghello, S., and Merlo, M. (2020). A Game Theoretic Approach for Energy Sharing in the Italian Renewable Energy Communities. Appl. Sci., 10.","DOI":"10.3390\/app10228166"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Kuhn, H.W., and Tucker, A.W. (1953). Contributions to the Theory of Games, Princeton University Press. Annals of Mathematical Studies, 28.","DOI":"10.1515\/9781400881970"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/s003550000070","article-title":"The value of a player in n-person games","volume":"18","author":"Hausken","year":"2001","journal-title":"Soc. Choice Welf."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/j.jet.2006.09.008","article-title":"Null or nullifying players: The difference between the Shapley value and equal division solutions","volume":"136","year":"2007","journal-title":"J. Econ. Theory"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.enpol.2018.01.045","article-title":"A Brazilian perspective of power systems integration using OSeMOSYS SAMBA\u2014South America Model Base\u2014And the bargaining power of neighbouring countries: A cooperative games approach","volume":"115","author":"Legey","year":"2018","journal-title":"Energy Policy"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/S0899-8256(05)80008-9","article-title":"On axiomatizations of the weighted Shapley values","volume":"8","author":"Nowak","year":"1995","journal-title":"Games Econ. Behav."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/BF01240278","article-title":"On the symmetric and weighted shapley values","volume":"20","author":"Chun","year":"1991","journal-title":"Int. J. Game Theory"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1129846","DOI":"10.3389\/fenrg.2023.1129846","article-title":"Weighted shapley value: A cooperative game theory for loss allocation in distribution systems","volume":"11","author":"Pal","year":"2023","journal-title":"Front. Energy Res."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"102459","DOI":"10.1016\/j.jmateco.2020.102459","article-title":"Weakly balanced contributions and the weighted Shapley values","volume":"94","author":"Casajus","year":"2021","journal-title":"J. Math. Econ."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"4568","DOI":"10.1109\/TPWRS.2013.2278296","article-title":"Transmission Network Cost Allocation Based on Circuit Theory and the Aumann-Shapley Method","volume":"28","author":"Molina","year":"2013","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1109\/TPWRS.2007.907133","article-title":"An Aumann-Shapley Approach to Allocate Transmission Service Cost Among Network Users in Electricity Markets","volume":"22","author":"Junqueira","year":"2007","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1109\/TPWRS.2009.2016376","article-title":"Allocation of Firm-Energy Rights among Hydro Plants: An Aumann\u2013Shapley Approach","volume":"24","author":"Faria","year":"2009","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1016\/j.energy.2016.10.135","article-title":"Estimating the benefits of transmission expansion projects: An Aumann-Shapley approach","volume":"118","author":"Olmos","year":"2017","journal-title":"Energy"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1137\/0117107","article-title":"The nucleolus of a characteristic function game","volume":"17","author":"Schmeidler","year":"1969","journal-title":"SIAM J. Appl. Math."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1109\/TPWRS.2003.810903","article-title":"Cost assignment model for electrical transmission system expansion: An approach through the Kernel theory","volume":"18","author":"Evans","year":"2003","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Espe, E., Potdar, V., and Chang, E. (2018). Prosumer Communities and Relationships in Smart Grids: A Literature Review, Evolution and Future Directions. Energies, 11.","DOI":"10.3390\/en11102528"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MWC.017.2100187","article-title":"Empowering Prosumer Communities in Smart Grid with Wireless Communications and Federated Edge Learning","volume":"28","author":"Taik","year":"2021","journal-title":"IEEE Wirel. Commun."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"1790","DOI":"10.1109\/TSG.2015.2508443","article-title":"Price Discrimination for Energy Trading in Smart Grid: A Game Theoretic Approach","volume":"8","author":"Tushar","year":"2017","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"117243","DOI":"10.1016\/j.apenergy.2021.117243","article-title":"Fully decentralized peer-to-peer energy sharing framework for smart buildings with local battery system and aggregated electric vehicles","volume":"299","author":"Lyu","year":"2021","journal-title":"Appl. Energy"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"1585","DOI":"10.1109\/TII.2015.2426052","article-title":"Optimal Pricing and Energy Scheduling for Hybrid Energy Trading Market in Future Smart Grid","volume":"11","author":"Wu","year":"2015","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1016\/j.procs.2019.09.249","article-title":"On framework development for the dynamic prosumer coalition in a smart grid and its evaluation by analytic tools","volume":"159","author":"Sumesh","year":"2019","journal-title":"Procedia Comput. Sci."},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Bayram, I.S., Shakir, M.Z., Abdallah, M., and Qaraqe, K. (2014, January 3\u20135). A Survey on Energy Trading in Smart Grid. Proceedings of the 2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Atlanta, GA, USA.","DOI":"10.1109\/GlobalSIP.2014.7032118"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"1398","DOI":"10.1109\/JSAC.2014.2332112","article-title":"Direct electricity trading in smart grid: A coalitional game analysis","volume":"32","author":"Lee","year":"2014","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.ijepes.2004.08.009","article-title":"Transmission expansion cost allocation based on cooperative game theory for congestion relief","volume":"27","author":"Erli","year":"2005","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1016\/j.apenergy.2017.03.061","article-title":"Beneficiaries of transmission expansion projects of an expansion plan: An Aumann-Shapley approach","volume":"195","author":"Olmos","year":"2017","journal-title":"Appl. Energy"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"2486","DOI":"10.1109\/TSG.2016.2552642","article-title":"Cooperative Planning of Renewable Generations for Interconnected Microgrids","volume":"7","author":"Wang","year":"2016","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1109\/JIOT.2014.2363834","article-title":"PHEV Charging and Discharging Cooperation in V2G Networks: A Coalition Game Approach","volume":"1","author":"Yu","year":"2014","journal-title":"IEEE Internet Things J."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1049\/iet-gtd.2019.0070","article-title":"Optimal placement of DG units for the enhancement of MG networks performance using coalition game theory","volume":"14","author":"Karimizadeh","year":"2020","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Gautam, M., Bhusal, N., and Benidris, M. (2021, January 14\u201316). A cooperative game theory-based approach to sizing and siting of distributed energy resources. Proceedings of the 2021 North American Power Symposium (NAPS), College Station, TX, USA.","DOI":"10.1109\/NAPS52732.2021.9654578"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"106262","DOI":"10.1016\/j.epsr.2020.106262","article-title":"Optimal planning of clustered microgrid using a technique of cooperative game theory","volume":"183","author":"Ali","year":"2020","journal-title":"Electr. Power Syst. Res."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"100831","DOI":"10.1016\/j.est.2019.100831","article-title":"Optimal planning of PEV fast charging stations using nash bargaining theory","volume":"25","author":"Pahlavanhoseini","year":"2019","journal-title":"J. Energy Storage"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1016\/j.renene.2015.01.056","article-title":"Economic evaluation of batteries planning in energy storage power stations for load shifting","volume":"78","author":"Han","year":"2015","journal-title":"Renew. Energy"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1109\/TPWRS.2011.2175254","article-title":"A novel policy for locational marginal price calculation in distribution systems based on loss reduction allocation using game theory","volume":"27","author":"Shaloudegi","year":"2012","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"100371","DOI":"10.1016\/j.segan.2020.100371","article-title":"Cooperative energy management system for networked microgrids","volume":"23","author":"Querini","year":"2020","journal-title":"Sustain. Energy Grids Netw."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.energy.2019.03.154","article-title":"Game-theoretic planning for integrated energy system with independent participants considering ancillary services of power-to-gas stations","volume":"176","author":"Zhang","year":"2019","journal-title":"Energy"},{"key":"ref_99","doi-asserted-by":"crossref","unstructured":"Pourahmadi, F., Fotuhi-Firuzabad, M., and Dehghanian, P. (2016, January 2\u20136). Identification of critical components in power systems: A game theory application. Proceedings of the 2016 IEEE Industry Applications Society Annual Meeting, Portland, OR, USA.","DOI":"10.1109\/IAS.2016.7731953"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"100890","DOI":"10.1016\/j.segan.2022.100890","article-title":"A cooperative game theory-based approach to formulation of distributed slack buses","volume":"32","author":"Gautam","year":"2022","journal-title":"Sustain. Energy Grids Netw."},{"key":"ref_101","doi-asserted-by":"crossref","unstructured":"Gautam, M., Bhusal, N., and Benidris, M. (2021, January 26\u201329). A cooperative game theory-based approach to under-frequency load shedding control. Proceedings of the IEEE Power & Energy Society General Meeting (PESGM), Washington, DC, USA.","DOI":"10.1109\/PESGM46819.2021.9638191"},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1109\/TSG.2020.3015088","article-title":"Scaling up cooperative game theory-based energy management using prosumer clustering","volume":"12","author":"Han","year":"2020","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1109\/TDSC.2015.2415489","article-title":"Bayesian coalition negotiation game as a utility for secure energy management in a vehicles-to-grid environment","volume":"13","author":"Kumar","year":"2016","journal-title":"IEEE Trans. Dependable Secur. Comput."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.ijepes.2017.11.027","article-title":"Application of game theoretic approaches for identification of critical parameters affecting power system small-disturbance stability","volume":"97","author":"Hasan","year":"2018","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"101095","DOI":"10.1016\/j.segan.2023.101095","article-title":"A graph theory and coalitional game theory-based pre-positioning of movable energy resources for enhanced distribution system resilience","volume":"35","author":"Gautam","year":"2023","journal-title":"Sustain. Energy Grids Netw."},{"key":"ref_106","unstructured":"(2023, October 20). Peer-to-Peer Electricity Trading: Innovation Landscape Brief. International Renewable Energy Agency (IRENA). Available online: https:\/\/www.irena.org\/-\/media\/Files\/IRENA\/Agency\/Publication\/2020\/Jul\/IRENA_Peer-to-peer_electricity_trading_2020.pdf."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1109\/TCNS.2021.3113269","article-title":"Payoff Distribution in Robust Coalitional Games on Time-Varying Networks","volume":"9","author":"Raja","year":"2022","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"51519","DOI":"10.1109\/ACCESS.2021.3069416","article-title":"Consumer Flexibility Aggregation Using Partition Function Games with Non-Transferable Utility","volume":"9","author":"Pinto","year":"2021","journal-title":"IEEE Access"},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"108931","DOI":"10.1016\/j.ijepes.2022.108931","article-title":"Peer-to-peer energy trading market considering renewable energy uncertainty and participants\u2019 individual preferences","volume":"148","author":"Xia","year":"2023","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_110","doi-asserted-by":"crossref","unstructured":"Belgioioso, G., Ananduta, W., Grammatico, S., and Ocampo-Martinez, C. (2020, January 12\u201315). Energy Management and Peer-to-peer Trading in Future Smart Grids: A Distributed Game-Theoretic Approach. Proceedings of the 2020 European Control Conference (ECC), St. Petersburg, Russia.","DOI":"10.23919\/ECC51009.2020.9143658"},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1049\/iet-cps.2018.5046","article-title":"Market-based generator cost functions for power system test cases","volume":"3","author":"Durvasulu","year":"2018","journal-title":"IET Cyber-Phys. Syst. Theory Appl."},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"2854","DOI":"10.1049\/iet-gtd.2017.1496","article-title":"Estimating B-coefficients of power loss formula considering volatile power injections: An enhanced least square approach","volume":"12","author":"Liu","year":"2018","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"120","DOI":"10.7763\/JOCET.2016.V4.264","article-title":"Fuel Cost Optimization of an Islanded Microgrid Considering Environmental Impact","volume":"4","author":"Raj","year":"2016","journal-title":"J. Clean Energy Technol."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1016\/j.energy.2018.10.087","article-title":"Dynamic economic dispatch using complementary quadratic programming","volume":"166","author":"McLarty","year":"2019","journal-title":"Energy"},{"key":"ref_115","first-page":"523806","article-title":"Application of the Firefly Algorithm for Solving the Economic Emissions Load Dispatch Problem","volume":"2011","author":"Apostolopoulos","year":"2010","journal-title":"Int. J. Comb."},{"key":"ref_116","first-page":"8955","article-title":"Combined economic emission dispatch in hybrid power systems using competitive swarm optimization","volume":"34","author":"Mohapatra","year":"2022","journal-title":"J. King Saud Univ.-Comput. Inf. Sci."},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"6461690","DOI":"10.1155\/2022\/6461690","article-title":"Combined Economic Emission Dispatch of Microgrid with the Incorporation of Renewable Energy Sources Using Improved Mayfly Optimization Algorithm","volume":"2022","author":"Nagarajan","year":"2022","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"1754","DOI":"10.1016\/j.scient.2012.02.030","article-title":"Combined economic and emission dispatch solution using gravitational search algorithm","volume":"19","author":"Duman","year":"2012","journal-title":"Sci. Iran."},{"key":"ref_119","first-page":"447","article-title":"Solution of combined economic and emission dispatch problem using a novel chaotic improved harmony search algorithm","volume":"6","author":"Rezaie","year":"2019","journal-title":"J. Comput. Des. Eng."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"1976092","DOI":"10.1080\/08839514.2021.1976092","article-title":"Solution of combined economic and emission dispatch problems of power systems without penalty","volume":"36","author":"Zaoui","year":"2022","journal-title":"Appl. Artif. Intell."},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1016\/j.energy.2018.06.137","article-title":"Modified harmony search algorithm for combined economic emission dispatch of microgrid incorporating renewable sources","volume":"159","author":"Elattar","year":"2018","journal-title":"Energy"},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"2173","DOI":"10.1007\/s00521-016-2795-5","article-title":"An economic load dispatch and multiple environmental dispatch problem solution with microgrids using interior search algorithm","volume":"30","author":"Trivedi","year":"2018","journal-title":"Neural Comput. Appl."},{"key":"ref_123","doi-asserted-by":"crossref","unstructured":"Zhang, B., Du, Y., Lim, E.G., Jiang, L., and Yan, K. (2019, January 26\u201329). Design and Simulation of Peer-to-Peer Energy Trading Framework with Dynamic Electricity Price. Proceedings of the 2019 29th Australasian Universities Power Engineering Conference (AUPEC), Nadi, Fiji.","DOI":"10.1109\/AUPEC48547.2019.211948"},{"key":"ref_124","doi-asserted-by":"crossref","unstructured":"Long, C., Wu, J., Zhang, C., Thomas, L., Cheng, M., and Jenkins, N. (2017, January 16\u201320). Peer-to-peer energy trading in a community microgrid. Proceedings of the 2017 IEEE Power & Energy Society General Meeting, Chicago, IL, USA.","DOI":"10.1109\/PESGM.2017.8274546"},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.epsr.2013.07.006","article-title":"Optimization of economic\/emission load dispatch for hybrid generating systems using controlled Elitist NSGA-II","volume":"105","year":"2013","journal-title":"Electr. Power Syst. Res."},{"key":"ref_126","unstructured":"Al-Roomi, A.R. (2023, October 20). Economic Load Dispatch Test Systems Repository, Halifax, Nova Scotia, Canada: Dalhousie University, Electrical and Computer Engineering. Available online: https:\/\/al-roomi.org\/economic-dispatch\/6-units-system\/system-i."},{"key":"ref_127","doi-asserted-by":"crossref","unstructured":"Zaraki, A., and Othman, M.F.B. (2009, January 4\u20137). Implementing Particle Swarm Optimization to Solve Economic Load Dispatch Problem. Proceedings of the 2009 International Conference of Soft Computing and Pattern Recognition, Malacca, Malaysia.","DOI":"10.1109\/SoCPaR.2009.24"},{"key":"ref_128","unstructured":"(2023, October 20). Eurostat, Databse. Available online: https:\/\/ec.europa.eu\/eurostat\/statistics-explained\/index.php?title=Electricity_price_statistics."},{"key":"ref_129","unstructured":"(2023, October 20). OECD.Stat, Database. Available online: https:\/\/stats.oecd.org\/Index.aspx?DataSetCode=RE_FIT#."},{"key":"ref_130","doi-asserted-by":"crossref","unstructured":"Bhandari, R., Arce, B.E., Sessa, V., and Adamou, R. (2021). Sustainability Assessment of Electricity Generation in Niger Using a Weighted Multi-Criteria Decision Approach. Sustainability, 13.","DOI":"10.3390\/su13010385"},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1016\/j.rser.2014.09.018","article-title":"Using a sustainability index to assess energy technologies for rural electrification","volume":"41","author":"Mainali","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.enpol.2017.09.022","article-title":"Life cycle sustainability assessment of electricity generation in Pakistan: Policy regime for a sustainable energy mix","volume":"111","author":"Akber","year":"2017","journal-title":"Energy Policy"},{"key":"ref_133","doi-asserted-by":"crossref","first-page":"110464","DOI":"10.1016\/j.jenvman.2020.110464","article-title":"Sustainability assessment of energy production: A critical review of methods, measures and issues","volume":"264","author":"Turkson","year":"2020","journal-title":"J. Environ. Manag."},{"key":"ref_134","doi-asserted-by":"crossref","first-page":"102638","DOI":"10.1016\/j.omega.2022.102638","article-title":"Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management","volume":"110","author":"Luo","year":"2022","journal-title":"Omega"},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/j.ejor.2013.02.034","article-title":"Cooperative game theory approach to allocating benefits of horizontal cooperation","volume":"229","author":"Lozano","year":"2013","journal-title":"Eur. J. Oper. Res."},{"key":"ref_136","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.apenergy.2018.03.086","article-title":"A cooperative game approach for coordinating multi-microgrid operation within distribution systems","volume":"222","author":"Du","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_137","doi-asserted-by":"crossref","first-page":"3265","DOI":"10.1109\/TPWRS.2014.2374532","article-title":"A hybrid MILP and Benders decomposition approach to find the nucleolus quota allocation for a renewable energy portfolio","volume":"30","author":"Freire","year":"2015","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_138","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ijepes.2016.11.015","article-title":"Loss allocation of radial distribution system using Shapley value: A sequential approach","volume":"88","author":"Sharma","year":"2017","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_139","doi-asserted-by":"crossref","unstructured":"Han, L., Morstyn, T., Crozier, C., and McCulloch, M. (2019, January 23\u201327). Improving the Scalability of a Prosumer Cooperative Game with K-Means Clustering. Proceedings of the 2019 IEEE Milan PowerTech, Milan, Italy.","DOI":"10.1109\/PTC.2019.8810558"},{"key":"ref_140","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.1109\/COMST.2017.2698366","article-title":"A Survey on Modeling and Optimizing Multi-Objective Systems","volume":"19","author":"Cho","year":"2017","journal-title":"IEEE Commun. Surv. Tutor."}],"container-title":["Energies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1073\/16\/24\/8115\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:40:26Z","timestamp":1760132426000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1073\/16\/24\/8115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,17]]},"references-count":140,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["en16248115"],"URL":"https:\/\/doi.org\/10.3390\/en16248115","relation":{},"ISSN":["1996-1073"],"issn-type":[{"value":"1996-1073","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,17]]}}}