An evolutionary game model for coordinated emergency material reserve considering public participation

doi:10.16265/j.cnki.issn1003-3033.2026.07.0801

Abstract

Abstract:

To optimize the emergency material reserve system and enhance the effectiveness of emergency response, a four-party evolutionary game model for collaborative emergency material reserve was constructed, incorporating the government, the emergency industry, the media, and the public, with public participation taken into consideration. The asymptotically stable points of the system and their conditional constraints were determined, and the evolutionary stability strategies were analyzed through numerical simulation. The results show that multiple evolutionary stability strategies exist in the system, which can be mapped to potential scenarios of multi-agent collaborative reserve. It is concluded that the government should guide the public to reserve emergency materials reasonably based on regional risk characteristics. Against the backdrop of frequent emergencies, the government should draw on the supply guarantee model of Shimian County in Ya'an, Sichuan, and the flood and typhoon prevention experience of Zhejiang Province, and enhance public acceptance and awareness of independent reserve through media science publicity and policy guidance. In the context of routine risk response, the government should refer to the experience of Weifang in Shandong Province in establishing an emergency industry alliance, give full play to the market role of the emergency industry, and promote active reserve behavior among the public through media advertising and experiential publicity.

Key words: public participation, emergency material, collaborative reserve, evolutionary game, emergency

CLC Number:

X928.03事故预防与预测

Lei Ting, Hui Xiaojing. An evolutionary game model for coordinated emergency material reserve considering public participation[J]. China Safety Science Journal, 2026, 36(7): 207-215.

Figures/Tables 13

Fig.1

Table 1

Table 2

Table 3

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

References 11

[1]	李慧, 滕五晓. 场域理论视角下民众应急准备能力建设路径探索[J]. 宁夏社会科学, 2022(4):78-83.
[2]	扈衷权, 田军, 冯耕中. 基于协议企业生产能力储备的应急物资采购定价模型[J]. 管理评论, 2021, 33(9):294-303.
	Hu Zhongquan, Tian Jun, Feng Gengzhong. The pricing model of emergency supplies purchasing based on production capacity reserve[J]. Management Review, 2021, 33(9):294-303.
[3]	冯晖, 黄承锋, 张立, 等. 不对称信息下应急物资储备与合同设计研究[J]. 中国管理科学, 2023, 31(12):117-127. doi: 10.16381/j.cnki.issn1003-207x.2021.1222
	Feng Hui, Huang Chengfeng, Zhang Li, et al. The research on emergency material reserve and contract design under asymmetric information[J]. Chinese Journal of Management Science, 2023, 31(12):117-127. doi: 10.16381/j.cnki.issn1003-207x.2021.1222
[4]	Liu Yang, Tian Jun, Feng Gengzhong, et al. A relief supplies purchasing model via option contracts[J]. Computers & Industrial Engineering, 2019, 137: DOI:10.1016/j.cie.2019.106009.
[5]	Miao Qing, Zhang Fengxiu. Drivers of household preparedness for natural hazards: the mediating role of perceived coping efficacy[J]. Natural Hazards Review, 2023, 24(2): DOI:10.1061/NHREFO.NHENG-1620.
[6]	Yin Xiangju, Yu Yongli, Kang Yifan, et al. A cross-sectional study on household disaster preparedness in China and analysis of its influencing factors[J]. BMC Public Health, 2025, 25(1): DOI:10.1186/s12889-025-23281-3.
[7]	唐建兵, 李芳, 施可可. 基于三方演化博弈的应急物资物价稳定性研究[J]. 物流工程与管理, 2023, 45(8):7-12,6.
	Tang Jianbing, Li Fang, Shi Keke. Research on price stability of emergency supplies based on tripartite evolutionary game[J]. Logistics Engineering and Management, 2023, 45(8):7-12,6.
[8]	Wu Shiwen, Shen Yanfang, Geng Yujie, et al. Consumer panic buying behavior and supply distribution strategy in a multiregional network after a sudden disaster[J]. Systems, 2023, 11(2): DOI:10.3390/systems11020110.
[9]	Selten R. A note on evolutionarily stable strategies in asymmetric animal conflicts[J]. Journal of Theoretical Biology, 1980, 84(1): 93-101. pmid: 7412323
[10]	邵舒羽, 刘艳, 王晴, 等. 非常规突发事件下应急物资储备政企协同演化博弈[J]. 中国安全科学学报, 2023, 33(4):210-220. doi: 10.16265/j.cnki.issn1003-3033.2023.04.0952
	Shao Shuyu, Liu Yan, Wang Qing, et al. Government-enterprise cooperative evolutionary game of emergency material reserve under unconventional emergency events[J]. China Safety Science Journal, 2023, 33(4):210-220. doi: 10.16265/j.cnki.issn1003-3033.2023.04.0952
[11]	伍佳妮, 刘之敬, 王莹. 期权契约机制下考虑社会捐赠的应急物资混合储备决策[J]. 中国安全科学学报, 2025, 35(7):225-232. doi: 10.16265/j.cnki.issn1003-3033.2025.07.0090
	Wu Jiani, Liu Zhijing, Wang Ying. Hybrid reserve decision-making for emergency supplies considering social donations under option contract mechanism[J]. China Safety Science Journal, 2025, 35(7):225-232.

策略选择		媒体 B	政府G
			强储备需求x		弱储备需求1-x
			公众L 强参与储备意愿o	公众弱参与储备意愿1-o	公众强参与储备意愿o	公众弱参与储备意愿1-o
应急产业 W	深合作 y	积极宣传 z	G₁=-P₂Q₂(1+π)(1-ε)-S+M(1-β) W₁=Q₂(P₂-C)(1+π)(1-ε)- K(1-ε)+Q₃(P₁-C)(1-ε)(1-δ) B₁=S+K(1-ε)+Q₃(P₁-C)(1-ε)δ L₁=ϕS+Kη-P₁Q₃(1-ε)	G₂=-P₂Q₂(1+π)(1-ε)-S W₂=Q₂(P₂-C)(1+π)(1-ε)- K(1-ε) B₂=S+K(1-ε) L₂=-(η-ε)(1+β)H	G₃=-P₁Q₁(1-ε)-T-βN W₃=Q₁(P₁-C)(1-ε)+T- K(1-ε)+Q₃(P₁-C)(1-ε)(1-δ) B₃=K(1-ε)+Q₃(P₁-C)(1-ε)δ L₃=Kη-P₁Q₃(1-ε)	G₄=-P₁Q₁(1-ε)-T W₄=Q₁(P₁-C)(1-ε)+T-K(1-ε) B₄=K(1-ε) L₄=-(η-ε)H
	深合作 y	消极宣传 1-z	G₅=-P₂Q₂(1+π)(1-ε)+ F(1+β)(1+ω)+M(1-β) W₅=Q₂(P₂-C)(1+π)(1-ε)- K(1-ε)+Q₃(P₁-C)(1-ε)(1-ω) B₅=-F(1+β)(1+ω)+K(1-ε)+ Q₃(P₁-C)(1-ε)ω L₅=-Kω-P₁Q₃(1-ε)	G₆=-P₂Q₂(1+π)(1-ε)+F(1+β) W₆=Q₂(P₂-C)(1+π)(1-ε)-K(1-ε) B₆=-F(1+β)+K(1-ε) L₆=(ω+ε)(1+β)H	G₇=-P₁Q₁(1-ε)-T+F(1+β)(1+ω)-βN W₇=Q₁(P₁-C)(1-ε)+T-K(1-ε)+ Q₃(P₁-C)(1-ε)(1-ω) B₇=-F(1+β)(1+ω)+K(1-ε)+ Q₃(P₁-C)(1-ε)ω L₇=-ωK-P₁Q₃(1-ε)	G₈=-P₁Q₁(1-ε)-T+F(1+β) W₈=Q₁(P₁-C)(1-ε)+T-K(1-ε) B₈=-F(1+β)+K(1-ε) L₈=(ω+ε)H
	浅合作 1-y	积极宣传 z	G₉=-P₂Q₂(1+π)-S+M(1-β) W₉=Q₂(P₂-C)(1+π)-K+ Q₃(P₁-C)(1-δ) B₉=S+K+Q₃(P₁-C)δ L₉=ϕS+Kη-P₁Q₃	G₁₀=-P₂Q₂(1+π)-S W₁₀=Q₂(P₂-C)(1+π)-K B₁₀=S+K L₁₀=-ηH(1+β)	G₁₁=-P₁Q₁-βN W₁₁=Q₁(P₁-C)-K+Q₃(P₁-C)(1-δ) B₁₁=K+Q₃(P₁-C)δ L₁₁=Kη-P₁Q₃	G₁₂=-P₁Q₁ W₁₂=Q₁(P₁-C)-K B₁₂=K L₁₂=-ηH
	浅合作 1-y	消极宣传 1-z	G₁₃=-P₂Q₂(1+π)+ F(1+β)(1+ω)+M(1-β) W₁₃=Q₂(P₂-C)(1+π)-K+ Q₃(P₁-C)(1-ω) B₁₃=-F(1+β)(1+ω)+K+ Q₃(P₁-C)ω L₁₃=-Kω-P₁Q₃	G₁₄=-P₂Q₂(1+π)+F(1+β) W₁₄=Q₂(P₂-C)(1+π)-K B₁₄=-F(1+β)+K L₁₄=ωH(1+β)	G₁₅=-P₁Q₁+F(1+β)(1+ω)-βN W₁₅=Q₁(P₁-C)-K+Q₃(P₁-C)(1-ω) B₁₅=-F(1+β)(1+ω)+K+Q₃(P₁-C)ω L₁₅=-Kω-P₁Q₃	G₁₆=-P₁Q₁+F(1+β) W₁₆=Q₁(P₁-C)-K B₁₆=-F(1+β)+K L₁₆=ωH

均衡点	特征值	符号	稳定条件
(1,0,1,0)	ε[K-Q₂(P₂-C)(1+π)],-S-F(1+β), S-P₁Q₁+P₂Q₂(1+π),ηK-P₁Q₃+ϕS+η(1+β)H	(×,-,×,×)	εK<εQ₂(P₂-C)(1+π),S+P₂Q₂(1+π)<P₁Q₁ ηK+ϕS+η(1+β)H<P₁Q₃
(1,0,1,1)	ε[K-Q₃(P₁-C)(1-δ)-Q₂(P₂-C)(1+π)], -Q₃(P₁-C)(δ-ω)-F(β+1)(ω+1)-S, P₁Q₃-ηK-ϕS-η(1+β)H,S-P₁Q₁- βN-M(1-β)+P₂Q₂(1+π)	(×,-,×,×)	εK<εQ₃(P₁-C)(1-δ)+εQ₂(P₂-C)(1+π) P₁Q₃<ηK+ϕS+η(1+β)H S+P₂Q₂(1+π)<P₁Q₁+βN+M(1-β)
(1,1,1,0)	-S-F(1+β),-ε[K-Q₂(P₂-C)(1+π)], S-T-[P₁Q₁-P₂Q₂(1+π)](1-ε), ηK+ϕS-P₁Q₃(1-ε)-ε(1+β)H+η(1+β)H	(-,×,×,×)	εQ₂(P₂-C)(1+π)<εK S+P₂Q₂(1+π)(1-ε)<T+P₁Q₁(1-ε) ηK+ϕS+η(1+β)H<P₁Q₃(1-ε)+ε(1+β)H
(1,1,1,1)	-ε[K-Q₃(P₁-C)(1-δ)-Q₂(P₂-C)(1+π)], -S-F(1+β)(1+ω)-Q₃(P₁-C)(δ-ω)(1-ε), ε(1+β)H-η(1+β)H-ϕS+(1-ε)P₁Q₃-ηK, S-T-βN-[P₁Q₁-P₂Q₂(1+π)](1-ε)-M(1-β)	(×,-,×,×)	εQ₃(P₁-C)(1-δ)+εQ₂(P₂-C)(1+π)<εK ε(1+β)H+(1-ε)P₁Q₃<ηK+ϕS+η(1+β)H S+P₂Q₂(1+π)(1-ε)<T+βN+ M(1-β)+P₁Q₁(1-ε)
(0,0,1,0)	T+ε[K-Q₁(P₁-C)],-F(β+1), -P₁Q₃+ηK+ηH,P₁Q₁-S-P₂Q₂(1+π)	(×,-,×,×)	T+εK<εQ₁(P₁-C),ηK+ηH<P₁Q₃ P₁Q₁<S+P₂Q₂(1+π)
(0,0,1,1)	-Q₃(P₁-C)(δ-ω)-F(β+1)(ω+1), T+ε[K-Q₁(P₁-C)-Q₃(P₁-C)(1-δ)], P₁Q₃-ηK-ηH,P₁Q₁-S+Nβ+M(1-β)-P₂Q₂(1+π)	(-,×,×,×)	T+εK<εQ₁(P₁-C)+εQ₃(P₁-C)(1-δ) P₁Q₃<ηK+ηH P₁Q₁+Nβ+M(1-β)<S+P₂Q₂(1+π)
(0,1,1,0)	-T-ε[K-Q₁(P₁-C)],ηK-εH+ηH-P₁Q₃(1-ε), -F(β+1),T-S+(1-ε)[P₁Q₁-P₂Q₂(1+π)]	(×,×,-,×)	εQ₁(P₁-C)<T+εK,ηK+ηH<εH+P₁Q₃(1-ε) T+(1-ε)P₁Q₁<S+(1-ε)P₂Q₂(1+π)
(0,1,1,1)	-T-ε[K-Q₁(P₁-C)-Q₃(P₁-C)(1-δ)], -F(β+1)(ω+1)-Q₃(P₁-C)(δ-ω)(1-ε), εH-ηH-ηK+P₁Q₃(1-ε), T-S+Nβ+(1-ε)[P₁Q₁-P₂Q₂(1+π)]+(1-β)M	(×,-,×,×)	εQ₁(P₁-C)+εQ₃(P₁-C)(1-δ)<T+εK εH+P₁Q₃(1-ε)<ηH+ηK T+Nβ+(1-ε)P₁Q₁+(1-β)M< S+(1-ε)P₂Q₂(1+π)

参数	赋值	参数	赋值	参数	赋值	参数	赋值
P₁	16	π	0.5	C	3	Q₃	10
Q₁	40	S	30	ε	0.6	F	60
T	35	M	100	K	100	ϕ	0.5
P₂	8	N	120	δ	0.5	η	0.5
Q₂	45	β	0.5	ω	0.3	H	90

[1]	Wang Qingmin, Deng Shuai. Research on public participation in safety regulation of hazardous materials transportation based on evolutionary game theory [J]. China Safety Science Journal, 2026, 36(7): 20-28.
[2]	Xiao Shangrui, Hu Jinqiu, Zhang Laibin. Safety resilience assessment for oil and gas reserve depots under sudden event disturbances [J]. China Safety Science Journal, 2026, 36(7): 216-224.
[3]	Tong Ruipeng, Wang Qian, Li Xinyang, Deng Yingqi, Hao Binxin. Independent knowledge system of China's emergency science:construction logic and practical paths [J]. China Safety Science Journal, 2026, 36(6): 1-8.
[4]	Chen Jianwu, Pan Lewenyu, Gao Jingqi, Li Qun, Guo Zaifu, Xu Jingge. Automatic structuring method for fire emergency rescue regulations [J]. China Safety Science Journal, 2026, 36(6): 186-193.
[5]	Liu Changshi, Liu Tao, Ma Jingyi, Wang Feng, He Ming, Tang Ke. Routing for truck-drone collaborative distribution in epidemic areas: balancing risk and efficiency [J]. China Safety Science Journal, 2026, 36(5): 260-269.
[6]	Zhou Yufeng, Cheng Jiahao, Pan Zimei, Liu Changshi. Dynamically coordinated routing optimization for mountainous forest fire emergency supply delivery using multi-modal vehicles [J]. China Safety Science Journal, 2026, 36(5): 270-278.
[7]	Song Yinghua, Xu Hongqian, Sang Xiaoyan. Construction and analysis of a unitary scenario for cascading evolution of emergencies [J]. China Safety Science Journal, 2026, 36(4): 184-193.
[8]	Wang Li, Wang Zhe, Guan Wenling, Zhang Jiaqi, Liu Chaolin, Meng Yuying. BP neural network-based personnel positioning-tracking-stationary alarm system for emergency rescue [J]. China Safety Science Journal, 2026, 36(4): 204-210.
[9]	Zhao Chenyang. Evaluation and empirical research on support capability of emergency resources for major disasters oriented to sustainable development [J]. China Safety Science Journal, 2026, 36(4): 220-227.
[10]	Sun Qixuan, Liu Yang, Jia Shun, Lu Jifeng, Tian Jun. Post-earthquake emergency supplies distribution route planning considering road conditions and demand urgency [J]. China Safety Science Journal, 2026, 36(4): 235-243.
[11]	LIU Yuanyuan, TAN Zefeng, HAN Shuang, XU Mengting. Emergency evacuation bus scheduling for toxic gas leakage scenarios [J]. China Safety Science Journal, 2026, 36(3): 186-193.
[12]	GUO Hanjun, ZHANG Yuebing, ZHOU Aitao. Research on scenario structured representation of accident disaster emergency rescue system:taking coal mine accident rescue as an example [J]. China Safety Science Journal, 2026, 36(2): 172-179.
[13]	LI Zhijian, SHE Jianjun, LU Cong, GUO Zihao, ZHOU Yilun. Evaluation of emergency management capability for construction safety accidents based on FRAM-BN [J]. China Safety Science Journal, 2026, 36(2): 199-208.
[14]	REN Lipeng, TONG Ruipeng. Evolutionary game research on multi-body dynamic governance of intelligent coal mine safety risks [J]. China Safety Science Journal, 2026, 36(2): 253-261.
[15]	LU Yi, SHANG Yuanwang, WANG Yuhang, YUE Danfeng. Impact of decision-makers' risk perception on emergency material allocation in flood disasters [J]. China Safety Science Journal, 2026, 36(1): 182-190.