物理-社会耦合系统下震后多方协同救援的微分博弈模型

doi:10.16381/j.cnki.issn1003-207x.2021.2073

摘要/Abstract

摘要：

地震灾害救援系统是一个涉及道路通行能力和多方参与的物理-社会复杂耦合系统。其中，物理系统中道路受损是影响救灾物资运输的重要因素之一，社会系统中政府和社会力量的协同治理成效决定了救灾效果。为提高物资运输效率和灾区救灾量，本文考虑道路通行能力构建政府和社会组织协同运输非合作救援模式、协同合作救援模式以及政府补贴模式的微分博弈模型，计算了三种模式下多方努力水平、补贴比例、救灾量和系统均衡收益。研究发现，在一定条件下，政府补贴作为一种激励机制，可提高社会组织救灾努力水平、实现双方救灾效益的帕累托改进。社会系统中三种救灾模式具有不同的耦合效果。其中，协同合作救援最优策略及整体最优收益均严格优于非合作和政府补贴两种模式。

关键词: 震后救援, 微分博弈, 物理-社会耦合系统, 道路通行能力, 协同运输

Abstract:

Under the dynamic change of road conditions and multi-party disaster coupling system， how to choose the disaster relief path according to the specific situation of road damage has become an urgent problem to be solved at present. Earthquake disasters and other emergencies show the characteristics of a complex physical-social coupling system. In addition， some sections of the road system appear functional failure under the action of strong earthquakes， which hinders the transport of relief supplies and evacuation of casualties. In the disaster coupling system， the government and social organizations need to participate in the rescue. First of all， in the early stage after the earthquake， it was difficult for the external rescue forces of the government to quickly enter the scene because of traffic interruption and poor information， while social forces could guide the people to carry out self-rescue and mutual rescue， but the continuous social forces occupied the rescue road， resulting in traffic congestion， “saving people will be saved by others” and other secondary disasters. Secondly， socialized disaster prevention and mitigation is an important direction of current and future disaster prevention and mitigation mechanism reform， the government and social organizations cooperate， not only effectively make up for the “government failure” defect， but also promote the stable development of society； Finally， to guarantee the amount of disaster relief required by the disaster area， the government has increased financial support for social organizations to relieve the pressure of disaster relief.According to the different input strategies of government and social organizations in disaster relief， three cooperation modes are summarized， namely non-cooperative rescue mode， cooperative rescue mode， and government subsidy mode. Then the differential game model of cooperative transportation between government and social organization is constructed. First， three differential game models of cooperative transportation between government and social organization are described. Secondly， the optimal level of the relief effort， subsidy ratio， amount of relief， and system equilibrium income of both sides of the game are obtained and analyzed. Thirdly， the balance strategies of the three modes are compared and analyzed. Finally， the sensitivity of key parameters to the equilibrium results is analyzed. It is found that three disaster relief modes have different coupling effects in the social system. Among them， the non-cooperative rescue mode is prone to fall into the “prisoner's dilemma” of not subsidizing weak participation. When the government and social organizations transition from non-cooperative relief mode to government subsidy mode， the Pareto improvement of relief efficiency can be realized. When the two parties choose to cooperate， the amount of disaster relief and the system equilibrium benefit is strictly superior to the non-cooperation and government subsidy modes. Three traffic situations in the physical system have the same coupling effect. Both the quantity and benefit of disaster relief under unblocked conditions are better than those under congestion and congestion conditions. In addition， the amount of disaster relief is affected by the joint efforts of the government and social organizations， and the amount of disaster relief increases with the increase of the input of one party. If social organizations predict that the government will increase relief spending， they will choose to maintain the original level of relief efforts to avoid unnecessary costs. In terms of case selection， the Lushan Earthquake in Sichuan Province in 2013 is selected as the case analysis object. Key parameter values are obtained from relevant authoritative organizations， such as Xinhua News Agency， China Youth Daily， and the website of the Ministry of Finance.Three modes of cooperative transportation between government and social organizations are summarized and the coupling results of physical and social systems after the earthquake are analyzed. Relevant research has certain theoretical reference significance for further improving the cooperative transportation of disaster relief materials after the earthquake.

Key words: post-earthquake relief, differential game, physical-social coupling systems, road capacity, co-transport

中图分类号:

C931

杨曼,刘德海. 物理-社会耦合系统下震后多方协同救援的微分博弈模型[J]. 中国管理科学, 2024, 32(1): 115-124.

Man Yang,Dehai Liu. Differential Game Model of Multi-party Cooperative Rescue after Earthquake in Physical-social Coupling System[J]. Chinese Journal of Management Science, 2024, 32(1): 115-124.

图/表 4

表1

模型符号及其含义"

符号	定义
$τ t$	t时刻灾区有效救灾量，且初始物资 $τ 0 = τ 0$ ，状态变量
$E G t$	t时刻政府救灾努力水平，决策变量
$E S t$	t时刻社会组织救灾努力水平，决策变量
$S 1$	政府补贴系数， $0 ≤ S 1 < 1$ ，决策变量
$η G$	政府救灾成本系数， $η G > 0$
$η S$	社会组织救灾成本系数， $η S > 0$
$C G t$	t时刻政府救灾成本
$C S t$	t时刻社会组织救灾成本
$α$	社会组织救灾努力对灾区救灾量的影响系数， $α > 0$
$β$	政府救灾努力对灾区救灾量的影响系数， $β > 0$
$γ$	道路损毁程度， $0 ≤ γ ≤ 1$
$δ$	物资衰减率， $0 < δ < 1$
$λ$	社会组织单位救灾努力对潜在经济活动的影响系数， $λ > 0$
$μ$	政府单位救灾努力对潜在经济活动的影响系数， $μ > 0$
$θ$	救灾物资对潜在经济活动的影响系数， $θ > 0$
$π 1$	社会组织单位救灾努力挽回的直接损失， $π 1 > 0$
$π 2$	政府单位救灾努力挽回的直接损失， $π 2 > 0$
$π G$	政府单位潜在经济活动产生的价值， $π G > 0$
$π S$	社会组织单位潜在经济活动产生的价值， $π S > 0$
$ρ$	贴现率， $ρ > 0$

表1

图1

图2

表2

关键参数对均衡结果的敏感性分析"

参数	$E G N * / E G B * / E G C *$	$E S N * / E S B * / E S C *$	$τ G N * / τ G B * / τ G C *$
$π G = 0.5 → 1.5$	↑↑↑	— ↑↑	↑↑↑
$π S = 0.5 → 1.5$	——↑	↑↑↑	↑↑↑
$π 1 = 0.172 → 0.518$	———	↑↑↑	↑↑↑
$π 2 = 0.172 → 0.518$	↑↑↑	———	↑↑↑
$λ = 0.086 → 0.26$	———	↑↑↑	↑↑↑
$μ = 0.413 → 1.241$	↑↑↑	———	↑↑↑
$θ = 0.25 → 0.75$	↑↑↑	↑↑↑	↑↑↑
$α = 0.2 → 0.6$	———	↑↑↑	↑↑↑
$β = 0.284 → 0.854$	↑↑↑	———	↑↑↑
$δ = 0.35 → 1.05$	↓↓↓	↓↓↓	↓↓↓
$ρ = 0.1 → 0.3$	↓↓↓	↓↓↓	↓↓↓
$η G = 0.052 → 0.158$	↓↓↓	———	↓↓↓
$η S = 0.447 → 1.343$	———	↓↓↓	↓↓↓

表2

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