群众的自组织资源调度已经成为应急管理中不可或缺的一个重要组成部分，如何优化调度活动并维持调度方案的稳定性是一个引起广泛关注的问题。本文在自组织资源调度中提出了一种合作-非合作博弈耦合的策略选择方法，以及非重叠和重叠联盟组建的调度模型，解决其中效用冲突问题以确保调度方案的稳定性。主要工作如下：

1．基于自组织资源调度的特点，定义了满足社会抑制性的特征函数，构造了基于Aumann–Dr`eze值的效用函数，提出了非重叠联盟组建的调度模型，以参与人在联盟中分配得到的收益来衡量非合作博弈中的激励效用，实现了合作与非合作博弈的耦合。

2. 根据效用函数，分别构造了精确势博弈和置换势博弈模型，确保自组织应急资源调度系统中纳什均衡和置换均衡的存在性，通过证明效用函数的非减性和子模性，得到了纳什均衡的次优率，实现了效用的一致性统一及调度方案的稳定。这是本文的重要创新点之一。

3. 通过定义受限策略集，描述了参与人的动态决策过程，并以吉林省长春市的自组织应急管理模式为例，运用二元对数线性学习算法设置了四个参数对比实验，并求解了最优的调度方案，验证了势博弈调度模型的可行性和有效性。

4. 构造基于带联盟结构的Banzhaf值的效用函数，提出了参与人重叠联盟组建的调度模型，推导了精确势博弈及其纳什均衡的次优率，进一步推广了求解稳定调度方案的一般性结论，揭示了效用函数与纳什均衡效率的关系，并在数值案例中得到了最优、最稳定的调度方案。

The self-organized resource scheduling of the masses has become an indispensable part of emergency management, and how to optimize self-organized emergency resource scheduling activities and maintain the stability of their scheduling schemes after an emergency is a widely concerned issue. This paper proposes a self-organized strategy selection method based on cooperative-non-cooperative game coupling, as well as a scheduling model for non-overlapping and overlapping coalition formation in self-organized resource scheduling, and solves the utility conflict to ensure the stability of the scheduling scheme. The main research works of this paper are as follows.

1．Based on the characteristics of self-organized resource scheduling, a characteristic function that satisfies social inhibition is defined, and the utility function based on Aumann-Dr`eze value is constructed. A scheduling model for non-overlapping coalition formation is proposed, which measures the incentive utility in non-cooperative games by the benefits allocated by players in the coalition, achieving coupling between cooperative and non cooperative games.

2. According to the utility function, the exact potential game and permutable potential game models were constructed to ensure the existence of Nash equilibrium and permutation equilibrium in the self-organized emergency resource scheduling system. By proving the non-decreasing and submodularity of the utility function, the suboptimal rate of Nash equilibrium was obtained, achieving the consistent control of utility and the stability of scheduling schemes. This is one of the important innovations of this paper.

3. By defining a constrianed decision set, the dynamic decision-making process of players is described. Taking the self-organized emergency management model in Changchun City of Jilin Province as an example, four parameter comparative experiments are set using the Binary log-linear learning algorithm, and the optimal scheduling scheme is solved to verify the feasibility and effectiveness of the potential game scheduling model.

4. A utility function based on Banzhaf value with coalition structure is constructed, and a scheduling model for overlapping coalition formation is proposed. The exact potential game and the suboptimal rate of Nash equilibrium are derived, further generalizing the general conclusion of solving stable scheduling schemes. The relationship between utility function and Nash equilibrium efficiency is revealed, and the optimal and most stable scheduling scheme is obtained in numerical cases.

[1]Kundu T, Sheu J B, Kuo H T. Emergency logistics management—Review and propositions for future research [J]. Transportation research part E: logistics and transportation review, 2022, 164: 102789.

[2]A. Nagurney, L. S. Nagurney. A mean-variance disaster relief supply chain network modelfor risk reduction with stochastic link costs, time targets, and demand uncertainty [J]. SocialResponsibility in Production & Supply Chain Management eJournal, 2016, 231-255.

[3]Zhang Z, Sarcevic A. Coordination mechanisms for self-organized work in an emergency communication center [J]. Proceedings of the ACM on Human-Computer Interaction, 2018, 2(CSCW): 1-21.

[4]杨虎，张东戈，黄匆等. 自组织应对“突发事件”协同模型 [J]. 系统工程与电子技术, 2012，34（10）：2069-2074.

[5]张惠，翟拉，彭林. 应急治理中自组织如何促进合作秩序生成？——基于大规模公众众包的分析 [J]. 中国行政管理，2023，39（12）：130-140.

[6]李琦. 自组织视阈下应急管理的社会参与 [J]. 理论月刊，2016（8）：130-134.

[7]Reynolds C W. Flocks, Herds and Schools: A Distributed Behavioral Model [J]. ACM SIGGRAPH Computer Graphics, 1987, 21(4): 25-34.

[8]龚志文，刘太刚. 公共危机中民众的自组织机制及其约束——以抗击新冠肺炎疫情为例 [J]. 天津行政学院学报，2021，23（2）：11-23.

[9]Yulong C, Jiao S, Zhizhong G, et al. Status and Challenges of Public Health Emergency Management in China Related to COVID-19 [J]. Frontiers in public health, 2020, 8: 250.

[10]Milan E, Enrico N, R. K C, et al. Help from the Sky: Leveraging UAVs for Disaster Management [J]. IEEE Pervasive Computing, 2017, 16 (1): 24-32.

[11]Lu (Lucy) Yan, Alfonso J. Pedraza‐Martinez.Social Media for Disaster Management: Operational Value of the Social Conversation [J]. Production and Operations Management, 2019, 28 (10): 2514-2532.

[12]Nagurney A, Salarpour M, Dong J, et al. A Stochastic Disaster Relief Game Theory Network Model [J]. SN Operations Research Forum, 2020, 1 (1): 231-244.

[13]Yurisch K A, Soto K R, Fuenzalida C R. Covid-19: Network effectiveness of intermunicipal self-organized response in Chile [J]. Transylvanian Review of Administrative Sciences, 2020, 16(SI): 5-23.

[14]Narahari Y. 博弈论与机制设计 [M]. 北京：中国人民大学出版社，2017.

[15]谭春桥，张强. 合作对策理论及应用 [M]. 北京：科学出版社，2011.

[16]Paccagnan D, Chandan R, Marden J R. Utility and mechanism design in multi-agent systems: An overview [J]. Annual Reviews in Control, 2022, 53: 315-328.

[17]Ashby W R. Principles of the self-organizing dynamic system [J]. The Journal of general psychology, 1947, 37(2): 125-128.

[18]Gorodetskii V I. Self-organization and multiagent systems: I. Models of multiagent self-organization [J]. Journal of Computer & Systems Sciences International, 2012, 51(2): 256-281.

[19]D’Amato L, Naldini F, Tibaldo V, et al. Towards self-organizing railway traffic management: concept and framework [J]. Journal of Rail Transport Planning & Management, 2024, 29: 100427.

[20]何嘉耀. 基于自组织与多智能体系统的城市形态与交通需求研究 [D]. 清华大学，2013.

[21]Hadeli K, Valckenaers P, Germain B S, et al. Emergent forecasting using a stigmergy approach in manufacturing coordination and control [C]// Engineering Self-organising Systems. Springer-Verlag, 2005: 210-226.

[22]Serugendo G, Gleizes M, Karageorgos A. Self-organization in multi-agent systems [J]. Knowledge Engineering Review, 2005, 20(2): 165-189.

[23]Carole B, Vincent C, Vincent H, et al. Applications of Self-Organising Multi-Agent Systems: An Initial Framework for Comparison [J]. Informatica, 2006, 30(1): 73-82.

[24]Sims M, Goldman C V, Lesser V R. Self-organization through bottom-up coalition formation [C]// The Second International Joint Conference on Autonomous Agents & Multiagent Systems, 2003: 867-874.

[25]王昊彤. 针对地面区域的敏捷卫星任务自组织方法研究 [D]. 哈尔滨工程大学, 2019.

[26]寇明延，熊华钢，李峭，何锋. 面向任务能力的自组织网络体系结构 [J]. 系统工程与电子技术，2013，35（5）：980-986.

[27]周菁. 自组织多机器人系统任务分配建模与设计 [D]. 西北工业大学, 2015.

[28]吴莹莹，丁肇红，刘华平，赵怀林，孙富春. 面向环境探测的多智能体自组织目标搜索算法 [J].智能系统学报，2020，15（2）：289-295.

[29]王勃，姚佩阳，贾方超，陈洁钰. 多无人机任务集结合作博弈优化自组织协同控制 [J]. 电光与控制，2014，21（11）：5-13.

[30]王训，王兆魁，张育林. 基于合作博弈的智能集群自主聚集策略 [J]. 国防科技大学学报，2017，39（2）：146-151.

[31]Badreldin M, Hussein A, Khamis A. A Comparative Study between Optimization and Market-Based Approaches to Multi-Robot Task Allocation [J]. Advances in Artificial Intelligence, 2013, 2013: 1-13.

[32]Khamis A, Hussein A, Elmogy A. Multi-robot task allocation: A review of the state-of-the-art [J]. Cooperative robots and sensor networks 2015, 2015: 31-51.

[33]Shi H Y, Wang W L, Kwok N M, et al. Game theory for wireless sensor networks: a survey [J]. Sensors, 2012, 12(7): 9055-9097.

[34]Yao W, Yongkang S, Yunhui L. Research on improved genetic simulated annealing algorithm for multi-UAV cooperative task allocation [J]. Journal of Physics: Conference Series, 2022, 2246 (1): 012081.

[35]Li M, Gao Y, Wang M, et al. Multi-objective Optimization for Multi-task Allocation in Mobile Crowd Sensing [J]. Procedia Computer Science, 2019, 155 (C): 360-368.

[36]Lee D, Zaheer A S, Kim J H. A Resource-Oriented, Decentralized Auction Algorithm for Multirobot Task Allocation [J]. IEEE Transactions on Automation Science and Engineering, 2015, 12 (4): 1469-1481.

[37]Bogomolnaia A, Jackson M O. The stability of hedonic coalition structures [J]. Games and Economic Behavior, 2002, 38(2): 201-230.

[38]Jang I, Shin H S, Tsourdos A. Anonymous hedonic game for task allocation in a large-scale multiple agent system [J]. IEEE Transactions on Robotics, 2018, 34(6): 1534-1548.

[39]Li P, Duan H. A potential game approach to multiple UAV cooperative search and surveillance [J]. Aerospace Science and Technology, 2017; 68: 403-415.

[40]Guoge T, Jiayuan Z, Jin Z, et al. Multi-type task allocation for multiple heterogeneous unmanned surface vehicles (USVs) based on the self-organizing map [J]. Applied Ocean Research, 2022, 126: 103262.

[41]Yang J, Yuan G, Longjiang Y, et al. Self-Organizing Method on Mission-Level Task Allocation of Large-Scale Remote Sensing Satellite Swarm [J]. International Journal of Aerospace Engineering, 2022, 2022: 9307837.

[42]Xianli Z, Guixin W. Deep Q networks-based optimization of emergency resource scheduling for urban public health events [J]. Neural computing & applications, 2022, 35 (12): 10-11.

[43]Manyi C. Scientific and Technological Innovation Rapid Emergency Resource Constraint-Improved Particle Swarm Optimization Project Scheduling Method [J]. Journal of Advanced Manufacturing Systems, 2023, 22 (1): 165-180.

[44]Zheng Y J, Chen S Y, Ling H F. Evolutionary optimization for disaster relief operations: A survey [J]. Applied Soft Computing, 2015, 27: 553-566.

[45]Wu L, Xiang X. Emergency Resource Scheduling During COVID-19 [J]. E3S Web of Conferences, 2021, 253: 01012.

[46]Seaberg D, Devine L, Zhuang J. A review of game theory applications in naturaldisaster management research [J]. Natural Hazards, 2017, 89(3): 1461-1483.

[47]Nagurney A, Flores EA, Soylu C. A generalized nash equilibrium network modelfor post-disaster humanitarian relief [J]. Transportation Research Part E: logistics andTransportation Review, 2016, 95: 1-18.

[48]Nagurney A, Salarpour M, Dong J, et al. A stochastic disaster relief game theory network model [J]. SN Operations Research Forum , 2020, 1(10): 1-33.

[49]Liu J, Bai J, Wu D. Medical supplies scheduling in major public health emergencies [J]. Transportation Research Part E: Logistics and Transportation Review, 2021, 154: 102464.

[50]Shehory O, Kraus S. Methods for task allocation via agent coalition formation [J]. Artificial intelligence, 1998, 101(1-2): 165-200.

[51]Mahdiraji H A, Razghandi E, Hatami-Marbini A. Overlapping coalition formation in game theory: A state-of-the-art review [J]. Expert Systems with Applications, 2021, 174: 114752.

[52]王松柏. 基于联盟博弈的多无人机协同任务分配研究 [D]. 北方工业大学, 2023.

[53]周瑜. 基于联盟形成博弈的任务分配方法研究 [D]. 扬州大学，2019.

[54]Zhou Y, Zhang Y, Li B. Coalition Formation Game for Task Allocation in the Social Network [C] // 2018 IEEE 22nd International Conference on Computer Supported Cooperative Work in Design (CSCWD). IEEE, 2018: 133-139.

[55]Naoki Iijima, Ayumi Sugiyama, Masashi Hayano, Toshiharu Sugawara. Adaptive Task Allocation Based on Social Utility and Individual Preference in Distributed Environments [J]. Procedia Computer Science, 2017, 112.

[56]苏军，陈怡林，张东煜. 应急管理中自组织任务分配的博弈模型与应用 [J]．西安科技大学学报，2022，42（5）：1046-1053.

[57]Hart S, Mas-Colell A. Potential, value, and consistency [J]. Econometrica: Journal of the Econometric Society, 1989: 589-614.

[58]Monderer D, Shapley L S. Potential games [J]. Games and Economic Behavior, 1996, 14(1): 124-143.

[59]Marden J R, Arslan G, Shamma J S. Cooperative control and potential games [J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2009, 39(6): 1393-1407.

[60]Rosenthal, R.W. A class of games possessing pure-strategy Nash equilibria [J]. International Journal of Game Theory, 1973, 2(1): 65-67.

[61]Gusev V V. Nash-stable coalition partition and potential functions in games with coalition structure [J]. European Journal of Operational Research, 2021, 295(3): 1180-1188.

[62]Gusev V V, Mazalov V V. Potential functions for finding stable coalition structures [J]. Operations Research Letters, 2019, 47(6): 478-482.

[63]Arslan G, Marden J R, Shamma J S. Autonomous vehicle-target assignment: A game-theoretical formulation [J]. Journal of Dynamic Systems Measurement and Control,2007, 129: 584-596.

[64]Wu H, Shang H. Potential game for dynamic task allocation in multi-agent system [J]. ISA transactions, 2020, 102: 208-220.

[65]Gusev V V. Cooperative congestion games: existence of a Nash-stable coalition structure [J]. Optimization Letters, 2022: 1-15.

[66]Zhang J, Lu J, Cao J, et al. Traffic congestion pricing via network congestion game approach [J]. Discrete & Continuous Dynamical Systems-Series S, 2021, 14(4): 1553-1567.

[67]鞠锴，冒泽慧，姜斌，马亚杰. 基于势博弈的异构多智能体系统任务分配和重分配[J]. 自动化学报，2022，48（10）：2416-2428.

[68]Sun C, Wang X, Qiu H, et al. Game theoretic self-organization in multi-satellite distributed task allocation [J]. Aerospace Science and Technology, 2021, 112: 106650.

[69]HAKEN H S. An Introduction: Non-equilibriumPhase Transitions and Self- organization in Physics [M]. CA: Chemistry and Biology, Springer-VerlagⅢ, 1983.

[70]Heylighen F. Self-organization in Communicating Groups: The Emergence of Coordination, Shared References and Collective Intelligence [M]. Springer Berlin Heidelberg, 2013: 117-149.

[71]吴彤. 自组织方法论研究 [M]. 北京：清华大学出版社，2001.

[72]周跃进，郝巳玥，张连敏等. 自组织团队特征分析 [J]. 管理学报，2010，7（8）：1159-1164, 1170.

[73]Theo Driessen. Cooperative Games, Solutions and Applications [M]. Springer, Dordrecht, 1988.

[74]Aumann R J, Dr`eze J. Cooperative games with coalition structures [J]. InternationalJournal of Game Theory, 1974, 3(4): 217-237.

[75]Harsanyi J C. Papers in Game Theory [J]. Springer Nature, 1982, 28: 44-70.

[76]H. Haken. 协同学：自然成功的奥秘 [M]. 戴鸣钟. 上海：上海科学普及出版社，1998.

[77]Fritz Charles E, Mathewson John H. Convergence Behavior in Disasters: A problem in Social Control—A Special Report Prepared for the Committee on Disaster Studies [R]. National Academy of Sciences, National Research Council, Washington, 1957.

[78]Tumer K, Wolpert D. An Introduction to Collective Intelligence [M]. Springer Berlin Heidelberg, 2004: 133-178.

[79]Vetta A. Nash equilibria in competitive societies, with applications to facilitylocation, traffic routing and auctions [J]. Proceedings of the 43rd Annual Symposiumon Foundations of Computer Science, 2002: 416-425.

[80]Liu J, Williams R K. Submodular optimization for coupled task allocationand intermittent deployment problems [J]. IEEE Robotics and Automation Letters, 2019, 4(4): 3169-3176.

[81]Qu G, Brown D, Li N. Distributed greedy algorithm for multi-agent taskassignment problem with submodular utility functions [J]. Automatica, 2019, 105: 206-215.

[82]Blume L E. The statistical mechanics of strategic interaction [J]. Games and economic behavior, 1993, 5(3): 387-424.

[83]Marden J R, Shamma J S. Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation [J]. Games and Economic Behavior, 2012, 75(2): 788-808.

[84]Shamma J S, Arslan G. Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria [J]. IEEE Transactions on Automatic Control, 2005, 50(3): 312-327.

Hart S, Mas-Colell A. A simple adaptive procedure leading to correlated equilibrium [J]. Econometrica, 2000, 68(5): 1127-1150.