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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2025  > In Press, Accepted Manuscript
H. Li, J. Li, L. Ran, L. Zheng, and T. Huang, “A survey of distributed algorithms for aggregative games,” IEEE/CAA J. Autom. Sinica, 2025. doi: 10.1109/JAS.2024.124998
Citation: H. Li, J. Li, L. Ran, L. Zheng, and T. Huang, “A survey of distributed algorithms for aggregative games,” IEEE/CAA J. Autom. Sinica, 2025. doi: 10.1109/JAS.2024.124998
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A Survey of Distributed Algorithms for Aggregative Games

doi: 10.1109/JAS.2024.124998
Funds:  This work was supported in part by the Fundamental Research Funds for the Central Universities (SWU-XDJH202312), in part by the National Natural Science Foundation of China (62173278), and in part by the Chongqing Science Fund for Distinguished Young Scholars (2024NSCQ-JQX0103)
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    Abstract
  • Game theory-based models and design tools have gained substantial prominence for controlling and optimizing behavior within distributed engineering systems due to the inherent distribution of decisions among individuals. In non-cooperative settings, aggregative games serve as a mathematical framework model for the interdependent optimal decision-making problem among a group of non-cooperative players. In such scenarios, each player’s decision is influenced by an aggregation of all players’ decisions. Nash equilibrium seeking in aggregative games has emerged as a vibrant topic driven by applications that harness the aggregation property. This paper presents a comprehensive overview of the current research on aggregative games with a focus on communication topology. A systematic classification is conducted on distributed algorithm research based on communication topologies such as undirected networks, directed networks, and time-varying networks. Furthermore, it sorts out the challenges and compares the algorithms’ convergence performance. It also delves into real-world applications of distributed optimization techniques grounded in aggregative games. Finally, it proposes several challenges that can guide future research directions.

     

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  • [1]
    Z. Deng, “Distributed algorithm design for aggregative games of euler-lagrange systems and its application to smart grids,” IEEE Trans. Cybernetics, vol. 52, no. 8, pp. 8315–8325, 2022. doi: 10.1109/TCYB.2021.3049462
    [2]
    P. Zhou, W. Wei, K. Bian, D. O. Wu, Y. Hu, and Q. Wang, “Private and truthful aggregative game for large-scale spectrum sharing,” IEEE Journal on Selected Areas in Communications, vol. 35, no. 2, pp. 463–477, 2017. doi: 10.1109/JSAC.2017.2659099
    [3]
    M. Kumar, V. Gupta, R. Kumar, and B. Panigrahi, “Customer oriented electric vehicle charging scheduling in day-ahead market via aggregative game model,” in 2018 8th IEEE India Int. Conf. on Power Electronics (IICPE). IEEE, 2018, doi: 10.1109/IICPE.2018.8709412.
    [4]
    J. F. Nash Jr, “Equilibrium points in n-person games,” Proc. the national academy of sciences, vol. 36, no. 1, pp. 48–49, 1950. doi: 10.1073/pnas.36.1.48
    [5]
    D. Cheng, T. Xu, F. He, and H. Qi, “On dynamics and Nash equilibriums of networked games,” IEEE/CAA Journal of Automatica Sinica, vol. 1, no. 1, pp. 10–18, 2014. doi: 10.1109/JAS.2014.7004614
    [6]
    M. Dindoš and C. Mezzetti, “Better-reply dynamics and global convergence to Nash equilibrium in aggregative games,” Games and Economic Behavior, vol. 54, no. 2, pp. 261–292, 2006. doi: 10.1016/j.geb.2004.12.001
    [7]
    M. K. Jensen, “Aggregative games and best-reply potentials,” Economic Theory, vol. 43, no. 1, pp. 45–66, 2010. doi: 10.1007/s00199-008-0419-8
    [8]
    M. Ye, D. Li, Q.-L. Han, and L. Ding, “Distributed Nash equilibrium seeking for general networked games with bounded disturbances,” IEEE/CAA Journal of Automatica Sinica, vol. 10, no. 2, pp. 376–387, 2022.
    [9]
    M. Mazouchi, M. B. Naghibi-Sistani, and S. K. H. Sani, “A novel distributed optimal adaptive control algorithm for nonlinear multi-agent differential graphical games,” IEEE/CAA Journal of Automatica Sinica, vol. 5, no. 1, pp. 331–341, 2017.
    [10]
    D. Martimort and L. Stole, “Representing equilibrium aggregates in aggregate games with applications to common agency,” Games and Economic Behavior, vol. 76, no. 2, pp. 753–772, 2012. doi: 10.1016/j.geb.2012.08.005
    [11]
    P. von Mouche and F. Quartieri, Equilibrium theory for Cournot oligopolies and related games. Springer, 2016.
    [12]
    N. S. Kukushkin, “Best response dynamics in finite games with additive aggregation,” Games and Economic Behavior, vol. 48, no. 1, pp. 94–110, 2004. doi: 10.1016/j.geb.2003.06.007
    [13]
    M. Ye, Q.-L. Han, L. Ding, and S. Xu, “Fully distributed Nash equilibrium seeking for high-order players with actuator limitations,” IEEE/CAA Journal of Automatica Sinica, vol. 10, no. 6, pp. 1434–1444, 2023. doi: 10.1109/JAS.2022.105983
    [14]
    P. Dubey, O. Haimanko, and A. Zapechelnyuk, “Strategic complements and substitutes, and potential games,” Games and Economic Behavior, vol. 54, no. 1, pp. 77–94, 2006. doi: 10.1016/j.geb.2004.10.007
    [15]
    D. Paccagnan, B. Gentile, F. Parise, M. Kamgarpour, and J. Lygeros, “Distributed computation of generalized Nash equilibria in quadratic aggregative games with affine coupling constraints,” in 2016 IEEE 55th Conf. on Decision and Control (CDC), 2016, pp. 6123–6128.
    [16]
    S. Grammatico, “Dynamic control of agents playing aggregative games with coupling constraints,” IEEE Trans. Automatic Control, vol. 62, no. 9, pp. 4537–4548, 2017. doi: 10.1109/TAC.2017.2672902
    [17]
    H. Li, W. Huang, Z. Duan, D. H. Mguni, K. Shao, J. Wang, and X. Deng, “A survey on algorithms for Nash equilibria in finite normal-form games,” Computer Science Review, vol. 51, p. 100613, 2024. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1574013723000801
    [18]
    M. Ye, Q.-L. Han, L. Ding, and S. Xu, “Distributed Nash equilibrium seeking in games with partial decision information: A survey,” Proc. the IEEE, vol. 111, no. 2, pp. 140–157, 2023. doi: 10.1109/JPROC.2023.3234687
    [19]
    J. Koshal, A. Nedić, and U. V. Shanbhag, “Distributed algorithms for aggregative games on graphs,” Operations Research, vol. 64, no. 3, pp. 680–704, 2016. doi: 10.1287/opre.2016.1501
    [20]
    C. Song, C. Wu, Z. Lv, F. Zhang, J. Li, and S. Yang, “Distributed heavy-ball Nash equilibrium seeking algorithm in aggregative games,” in 2020 39th Chinese Control Conf. (CCC), 2020, pp. 5019–5024.
    [21]
    G. Belgioioso and S. Grammatico, “Semi-decentralized Nash equilibrium seeking in aggregative games with separable coupling constraints and non-differentiable cost functions,” IEEE Control Systems Letters, vol. 1, no. 2, pp. 400–405, 2017. doi: 10.1109/LCSYS.2017.2718842
    [22]
    ——, “Semi-decentralized generalized Nash equilibrium seeking in monotone aggregative games,” IEEE Trans. Automatic Control, vol. 68, no. 1, pp. 140–155, 2023. doi: 10.1109/TAC.2021.3135360
    [23]
    S. Liang, P. Yi, and Y. Hong, “Distributed Nash equilibrium seeking of a class of aggregative games,” in 2017 13th IEEE Int. Conf. on Control and Automation (ICCA), 2017, pp. 58–63.
    [24]
    L. Wang, S. Liang, and Y. Hong, “Discrete-time algorithm for distributed Nash equilibrium seeking of a class of aggregative games,” in 2017 36th Chinese Control Conf. (CCC). IEEE, 2017, pp. 11325–11330.
    [25]
    M. Ye and G. Hu, “Game design and analysis for price-based demand response: An aggregate game approach,” IEEE Trans. cybernetics, vol. 47, no. 3, pp. 720–730, 2016.
    [26]
    C. Van Nguyen, P. H. Hoang, M. H. Trinh, B.-H. Lee, and H.-S. Ahn, “Distributed Nash equilibrium seeking of an aggregative game by a singular perturbed algorithm,” in 2017 Australian and New Zealand Control Conf. (ANZCC). IEEE, 2017, pp. 145–150.
    [27]
    Z. Deng and S. Liang, “Distributed algorithms for aggregative games of multiple heterogeneous Euler–Lagrange systems,” Automatica, vol. 99, pp. 246–252, 2019. doi: 10.1016/j.automatica.2018.10.041
    [28]
    C. De Persis and S. Grammatico, “Continuous-time integral dynamics for a class of aggregative games with coupling constraints,” IEEE Trans. Automatic Control, vol. 65, no. 5, pp. 2171–2176, 2020. doi: 10.1109/TAC.2019.2939639
    [29]
    G. Belgioioso and S. Grammatico, “A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games,” in 2018 IEEE Conf. on Decision and Control (CDC), 2018, pp. 3541–3546.
    [30]
    E. Benenati, W. Ananduta, and S. Grammatico, “On the optimal selection of generalized Nash equilibria in linearly coupled aggregative games,” in 2022 IEEE 61st Conf. on Decision and Control (CDC), 2022, pp. 6389–6394.
    [31]
    G. Chen, X. Zeng, P. Yi, and Y. Hong, “Distributed algorithm for generalized Nash equilibria seeking of network aggregative game,” in 2017 36th Chinese Control Conf. (CCC). IEEE, 2017, pp. 11319–11324.
    [32]
    S. Liang, P. Yi, and Y. Hong, “Distributed Nash equilibrium seeking for aggregative games with coupled constraints,” Automatica, vol. 85, pp. 179–185, 2017. doi: 10.1016/j.automatica.2017.07.064
    [33]
    G. Belgioioso, A. Nedić, and S. Grammatico, “Distributed generalized Nash equilibrium seeking in aggregative games under partial-decision information via dynamic tracking,” in 2019 IEEE 58th Conf. on Decision and Control (CDC), 2019, pp. 5948–5954.
    [34]
    D. Gadjov and L. Pavel, “Single-timescale distributed gne seeking for aggregative games over networks via forward-backward operator splitting,” IEEE Trans. Automatic Control, vol. 66, no. 7, pp. 3259–3266, 2021. doi: 10.1109/TAC.2020.3015354
    [35]
    Z. Deng, “Distributed generalized Nash equilibrium seeking algorithm for nonsmooth aggregative games,” Automatica, vol. 132, p. 109794, 2021. doi: 10.1016/j.automatica.2021.109794
    [36]
    Z. Zheng, Y. Zhang, B. Zhang, and R. Yin, “Distributed Nash equilibrium seeking of aggregative games for high-order systems,” in 2020 39th Chinese Control Conf. (CCC), 2020, pp. 4789–4794.
    [37]
    X. Cai, F. Xiao, and B. Wei, “Distributed strategy-updating rules for aggregative games of multi-integrator systems with coupled constraints,” Systems and Control Letters, vol. 170, p. 105401, 2022. doi: 10.1016/j.sysconle.2022.105401
    [38]
    F. Parise, B. Gentile, and J. Lygeros, “A distributed algorithm for almost-Nash equilibria of average aggregative games with coupling constraints,” IEEE Trans. Control of Network Systems, vol. 7, no. 2, pp. 770–782, 2020. doi: 10.1109/TCNS.2019.2944300
    [39]
    G. Xu, G. Chen, H. Qi, and Y. Hong, “Efficient algorithm for approximating Nash equilibrium of distributed aggregative games,” IEEE Trans. Cybernetics, vol. 53, no. 7, pp. 4375–4387, 2023. doi: 10.1109/TCYB.2022.3175831
    [40]
    Z. Deng and X. Nian, “Distributed algorithm design for aggregative games of disturbed multiagent systems over weight-balanced digraphs,” Int. Journal of Robust and Nonlinear Control, vol. 28, no. 17, pp. 5344–5357, 2018. doi: 10.1002/rnc.4316
    [41]
    ——, “Distributed generalized Nash equilibrium seeking algorithm design for aggregative games over weight-balanced digraphs,” IEEE Trans. Neural Networks and Learning Systems, vol. 30, no. 3, pp. 695–706, 2019. doi: 10.1109/TNNLS.2018.2850763
    [42]
    Y. Zhu, W. Yu, G. Wen, and G. Chen, “Distributed Nash equilibrium seeking in an aggregative game on a directed graph,” IEEE Trans. Automatic Control, vol. 66, no. 6, pp. 2746–2753, 2021. doi: 10.1109/TAC.2020.3008113
    [43]
    Z. Deng, “Distributed Nash equilibrium seeking for aggregative games with second-order nonlinear players,” Automatica, vol. 135, p. 109980, 2022. doi: 10.1016/j.automatica.2021.109980
    [44]
    F. Parise, S. Grammatico, B. Gentile, and J. Lygeros, “Distributed convergence to Nash equilibria in network and average aggregative games,” Automatica, vol. 117, p. 108959, 2020. doi: 10.1016/j.automatica.2020.108959
    [45]
    D. Paccagnan, B. Gentile, F. Parise, M. Kamgarpour, and J. Lygeros, “Nash and Wardrop equilibria in aggregative games with coupling constraints,” IEEE Trans. Automatic Control, vol. 64, pp. 1373–1388, 2019. doi: 10.1109/TAC.2018.2849946
    [46]
    D. Wang, P. Chen, M. Chen, J. Lian, and W. Wang, “Distributed Nash equilibrium seeking for aggregative games over weight-unbalanced digraphs,” in IFAC-PapersOnLine, 2022, pp. 90–95.
    [47]
    S. Arefizadeh and A. Nedić, “A distributed algorithm for aggregative games on directed communication graphs,” in 2022 IEEE 61st Conf. on Decision and Control (CDC), 2022, pp. 6407–6412.
    [48]
    X. F. Wang, X. M. Sun, A. R. Teel, and K. Z. Liu, “Distributed robust nash equilibrium seeking for aggregative games under persistent attacks: A hybrid systems approach,” Automatica, vol. 122, no. 3, p. 109255, 2020.
    [49]
    G. Belgioioso, A. Nedić, and S. Grammatico, “Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks,” IEEE Trans. Automatic Control, vol. 66, no. 5, pp. 2061–2075, 2021. doi: 10.1109/TAC.2020.3005922
    [50]
    G. Xu, G. Chen, H. Qi, and Y. Hong, “Distributed ϵ-Nash equilibrium seeking in aggregative games with approximation,” in 2022 American Control Conf. (ACC), 2022, pp. 1293–1298.
    [51]
    M. Shakarami, C. De Persis, and N. Monshizadeh, “Distributed dynamics for aggregative games: Robustness and privacy guarantees,” Int. Journal of Robust and Nonlinear Control, vol. 32, no. 9, pp. 5048–5069, 2022. doi: 10.1002/rnc.6077
    [52]
    T. Wang and P. Yi, “An optimal distributed algorithm with operator extrapolation for stochastic aggregative games,” in 2022 4th Int. Conf. on Industrial Artificial Intelligence (IAI), 2022.
    [53]
    J. Lei, P. Yi, and L. Li, “Distributed no-regret learning for stochastic aggregative games over networks,” in 2021 40th Chinese Control Conf. (CCC), 2021, pp. 7512–7519.
    [54]
    A. Kannan and U. V. Shanbhag, “Distributed computation of equilibria in monotone Nash games via iterative regularization techniques,” SIAM Journal on Optimization, vol. 22, no. 3, pp. 1177–1205, 2012.
    [55]
    J. Lei, U. V. Shanbhag, and J. Chen, “Distributed computation of Nash equilibria for monotone aggregative games via iterative regularization,” in 2020 59th IEEE Conf. on Decision and Control (CDC), 2020, pp. 2285–2290.
    [56]
    H. Kebriaei, S. J. Sadati-Savadkoohi, M. Shokri, and S. Grammatico, “Multipopulation aggregative games: equilibrium seeking via mean-field control and consensus,” IEEE Trans. Automatic Control, vol. 66, no. 12, pp. 6011–6016, 2021. doi: 10.1109/TAC.2021.3057063
    [57]
    X. Fang, G. Wen, J. Zhou, J. Lv, and G. Chen, “Distributed Nash equilibrium seeking for aggregative games with directed communication graphs,” IEEE Trans. Circuits and Systems I: Regular Papers, vol. 69, no. 8, pp. 3339–3352, 2022. doi: 10.1109/TCSI.2022.3168770
    [58]
    R. Zhu, J. Zhang, K. You, and T. Basar, “Asynchronous networked aggregative games,” Automatica, vol. 136, p. 110054, 2022. doi: 10.1016/j.automatica.2021.110054
    [59]
    P. Liu, K. Lu, F. Xiao, B. Wei, and Y. Zheng, “Online distributed learning for aggregative games with feedback delays,” IEEE Trans. Automatic Control, vol. 68, no. 10, pp. 6385–6392, 2023. doi: 10.1109/TAC.2023.3237781
    [60]
    M. Ye, G. Hu, L. Xie, and S. Xu, “Differentially private distributed Nash equilibrium seeking for aggregative games,” IEEE Trans. Automatic Control, vol. 67, no. 5, pp. 2451–2458, 2022. doi: 10.1109/TAC.2021.3075183
    [61]
    J. Wang, J. F. Zhang, and X. He, “Differentially private distributed algorithms for stochastic aggregative games,” Automatica, vol. 142, p. 110440, 2022. doi: 10.1016/j.automatica.2022.110440
    [62]
    Y. Lin, K. Liu, D. Han, and Y. Xia, “Statistical privacy-preserving online distributed Nash equilibrium tracking in aggregative games,” IEEE Trans. Automatic Control, vol. 69, no. 1, 2024.
    [63]
    G. Debreu, “A social equilibrium existence theorem,” Proc. the National Academy of Sciences, vol. 38, no. 10, pp. 886–893, 1952. doi: 10.1073/pnas.38.10.886
    [64]
    F. Parise, B. Gentile, S. Grammatico, and J. Lygeros, “Network aggregative games: Distributed convergence to Nash equilibria,” in 2015 54th IEEE Conf. on Decision and Control (CDC). IEEE, 2015, pp. 2295–2300.
    [65]
    A. Nedić and A. Olshevsky, “Distributed optimization over time-varying directed graphs,” IEEE Trans. Automatic Control, vol. 60, no. 3, pp. 601–615, 2015. doi: 10.1109/TAC.2014.2364096
    [66]
    A. Nedić, A. Olshevsky, and W. Shi, “Achieving geometric convergence for distributed optimization over time-varying graphs,” SIAM Journal on Optimization, vol. 27, no. 4, pp. 2597–2633, 2017. doi: 10.1137/16M1084316
    [67]
    S. Sundhar Ram, A. Nedić, and V. V. Veeravalli, “Distributed stochastic subgradient projection algorithms for convex optimization,” Journal of Optimization Theory and Applications, vol. 147, pp. 516–545, 2010. doi: 10.1007/s10957-010-9737-7
    [68]
    X.-F. Wang, A. R. Teel, K.-Z. Liu, and X.-M. Sun, “Stability analysis of distributed convex optimization under persistent attacks: A hybrid systems approach,” Automatica, vol. 111, p. 108607, 2020. doi: 10.1016/j.automatica.2019.108607
    [69]
    T. Wu, K. Yuan, Q. Ling, W. Yin, and A. H. Sayed, “Decentralized consensus optimization with asynchrony and delays,” IEEE Trans. Signal and Information Processing over Networks, vol. 4, no. 2, pp. 293–307, 2018. doi: 10.1109/TSIPN.2017.2695121
    [70]
    Y. Tian, Y. Sun, and G. Scutari, “Achieving linear convergence in distributed asynchronous multiagent optimization,” IEEE Trans. Automatic Control, vol. 65, no. 12, pp. 5264–5279, 2020. doi: 10.1109/TAC.2020.2977940
    [71]
    H. Li, H. Cheng, Z. Wang, and G.-C. Wu, “Distributed Nesterov gradient and havy-ball double accelerated asynchronous optimization,” IEEE Trans. Neural Networks and Learning Systems, vol. 32, no. 12, pp. 5723–5737, 2021. doi: 10.1109/TNNLS.2020.3027381
    [72]
    Z. Peng, Y. Xu, M. Yan, and W. Yin, “ARock: An algorithmic framework for asynchronous parallel coordinate updates,” SIAM Journal on Scientific Computing, vol. 38, no. 5, pp. 2851–2879, 2016. doi: 10.1137/15M1024950
    [73]
    P. Yi and L. Pavel, “Asynchronous distributed algorithms for seeking generalized Nash equilibria under full and partial-decision information,” IEEE Trans. Cybernetics, vol. 50, no. 6, pp. 2514–2526, 2020. doi: 10.1109/TCYB.2019.2908091
    [74]
    M. Ye, “On resilience against cyber-physical uncertainties in distributed Nash equilibrium seeking strategies for heterogeneous games,” IEEE/CAA Journal of Automatica Sinica, 2024. doi: 10.1109/JAS.2024.124803
    [75]
    G. Shao, X.-F. Wang, and R. Wang, “Distributed Nash equilibrium seeking of aggregative games under networked attacks,” Asian Journal of Control, vol. 24, no. 2, pp. 659–668, 2022. doi: 10.1002/asjc.2563
    [76]
    X.-F. Wang, A. R. Teel, X.-M. Sun, K.-Z. Liu, and G. Shao, “A distributed robust two-time-scale switched algorithm for constrained aggregative games,” IEEE Trans. Automatic Control, vol. 68, no. 11, pp. 6525–6540, 2023. doi: 10.1109/TAC.2023.3240981
    [77]
    J. Koshal, A. Nedić, and U. V. Shanbhag, “A gossip algorithm for aggregative games on graphs,” in 2012 IEEE 51st IEEE Conf. on Decision and Control (CDC). IEEE, 2012, pp. 4840–4845.
    [78]
    H. Chen, Y. Li, R. H. Louie, and B. Vucetic, “Autonomous demand side management based on energy consumption scheduling and instantaneous load billing: An aggregative game approach,” IEEE Trans. Smart Grid, vol. 5, no. 4, pp. 1744–1754, 2014. doi: 10.1109/TSG.2014.2311122
    [79]
    J. Hu, E. An, Q. Sun, and B. Huang, “Distributed multi-energy trading for energy internet: An aggregative game approach,” CSEE Journal of Power and Energy Systems, 2022. doi: 10.17775/CSEEJPES.2021.01990
    [80]
    G. Belgioioso, W. Ananduta, S. Grammatico, and C. Ocampo-Martinez, “Operationally-safe peer-to-peer energy trading in distribution grids: a game-theoretic market-clearing mechanism,” IEEE Trans. Smart Grid, vol. 13, no. 4, pp. 2897–2907, 2022. doi: 10.1109/TSG.2022.3158442
    [81]
    A. Joshi, H. Kebriaei, V. Mariani, and L. Glielmo, “Decentralized control of residential energy storage system for community peak shaving: A constrained aggregative game,” in 2021 IEEE Madrid PowerTech, 2021, doi: 10.1109/PowerTech46648.2021.949505.
    [82]
    P. Jacquot, C. Wan, O. Beaude, and N. Oudjane, “Efficient estimation of equilibria in large aggregative games with coupling constraints,” IEEE Trans. Automatic Control, vol. 66, no. 6, pp. 2762–2769, 2021. doi: 10.1109/TAC.2020.3008649
    [83]
    Z. Guo, Z. An, N. Wei, S. Liu, Q. Qi, D. Xing, D. Wang, and C. Deng, “Supply-demand interactive equilibrium model of multiple multi-energy parks based on aggregative game mechanism,” in 2021 IEEE 5th Conf. on Energy Internet and Energy System Integration (EI2), 2021, pp. 3981–3986.
    [84]
    G. Belgioioso and S. Grammatico, “On convexity and monotonicity in generalized aggregative games,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 14338–14343, 2017. doi: 10.1016/j.ifacol.2017.08.2011
    [85]
    Z. Liu, Q. Wu, S. Huang, L. Wang, M. Shahidehpour, and Y. Xue, “Optimal day-ahead charging scheduling of electric vehicles through an aggregative game model,” IEEE Trans. Smart Grid, vol. 9, no. 5, pp. 5173–5184, 2017.
    [86]
    D. Paccagnan, M. Kamgarpour, and J. Lygeros, “On aggregative and mean field games with applications to electricity markets,” in 2016 European Control Conf. (ECC), 2016, pp. 196–201.
    [87]
    C. Cenedese, F. Fabiani, M. Cucuzzella, J. M. A. Scherpen, M. Cao, and S. Grammatico, “Charging plug-in electric vehicles as a mixed-integer aggregative game,” in 2019 IEEE 58th Conf. on Decision and Control (CDC), 2019, pp. 4904–4909.
    [88]
    F. Fabiani, M. A. Tajeddini, H. Kebriaei, and S. Grammatico, “Local stackelberg equilibrium seeking in generalized aggregative games,” IEEE Trans. Automatic Control, vol. 67, no. 2, pp. 965–970, 2022. doi: 10.1109/TAC.2021.3077874
    [89]
    Y. Pei, Y. Tao, H. Gu, and J. Lu, “Distributed Nash equilibrium seeking for aggregative games with quantization constraints,” IEEE Trans. Circuits and Systems I: Regular Papers, vol. 70, no. 6, pp. 2537–2549, 2023. doi: 10.1109/TCSI.2023.3255559
    [90]
    B. G. Bakhshayesh and H. Kebriaei, “Decentralized equilibrium seeking of joint routing and destination planning of electric vehicles: A constrained aggregative game approach,” IEEE Trans. Intelligent Transportation Systems, vol. 23, no. 8, pp. 13265–13274, 2022. doi: 10.1109/TITS.2021.3123207
    [91]
    S. J. S. Savadkoohi, H. Kebriaei, and F. Aminifar, “Aggregative game for charging coordination of pevs in a network of parking lots,” in 2019 Smart Grid Conf. (SGC). IEEE, 2019, doi: 10.1109/SGC49328.2019.9056619.
    [92]
    E. Eslami, H. Kebriaei, H. Atrianfar, and F. Farhadi, “Incentive mechanism design for unicast service provisioning with network aggregative game,” IEEE Trans. Automatic Control, vol. 68, no. 1, pp. 572–579, 2023. doi: 10.1109/TAC.2022.3144132
    [93]
    P. Zhou, W. Wei, K. Bian, D. O. Wu, Y. Hu, and Q. Wang, “Private and truthful aggregative game for large-scale spectrum sharing,” IEEE Journal on Selected Areas in Communications, vol. 35, no. 2, pp. 463–477, 2017. doi: 10.1109/JSAC.2017.2659099
    [94]
    Y. Wu, J. Wu, M. Huang, and L. Shi, “Mean-field transmission power control in dense networks,” IEEE Trans. Control of Network Systems, vol. 8, no. 1, pp. 99–110, 2021. doi: 10.1109/TCNS.2020.3035762
    [95]
    J. F. Bonnans, J. Gianatti, and L. Pfeiffer, “A lagrangian approach for aggregative mean field games of controls with mixed and final constraints,” SIAM Journal on Control and Optimization, vol. 61, no. 1, pp. 105–134, 2023. doi: 10.1137/21M1407720
    [96]
    A. Dickson, “The effects of entry in bilateral oligopoly,” Games, vol. 4, no. 3, pp. 283–303, 2013. doi: 10.3390/g4030283
    [97]
    A. S. Chakrabarti and R. Lahkar, “An evolutionary analysis of growth and fluctuations with negative externalities,” Dynamic Games and Applications, vol. 8, pp. 733–760, 2018. doi: 10.1007/s13235-017-0234-6
    [98]
    Z. Shi, A. Bestavros, A. Orda, and D. Starobinski, “A game-theoretic analysis of shared/buy-in computing systems,” IEEE Open Journal of the Communications Society, vol. 1, pp. 190–204, 2020. doi: 10.1109/OJCOMS.2020.2969646
    [99]
    R. Lahkar and S. Mukherjee, “Dominant strategy implementation in a large population public goods game,” Economics Letters, vol. 197, p. 109616, 2020. doi: 10.1016/j.econlet.2020.109616
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