突发公共卫生事件中地方政府与社会公众间的演化博弈研究

doi:10.15960/j.cnki.issn.1007-6093.2021.04.001

摘要/Abstract

摘要：

近年来，突发公共卫生事件频发，社会公众与地方政府相互配合是及时、高效解决突发公共卫生事件的必然选择。本文以全球抗击新冠肺炎疫情为背景，讨论在突发公共卫生事件中社会公众与地方政府之间的博弈关系，基于有限理性假设，构建演化博弈模型，分析博弈双方决策行为的动态调整过程，得到在不同条件下社会公众和地方政府的演化稳定策略。同时，利用MATLAB进行仿真实验，分析在博弈过程中政府的奖惩、上级部门的处罚等主要因素对博弈双方策略选择的影响。研究结果表明，完善相关的补贴政策，普及疫情防控的相关法律法规，加大对社会公众随意流动、违反疫情相关规章制度的惩罚力度，提高对地方政府宽松防疫的处罚等措施可以有效促进社会公众和地方政府之间的相互协作，最终实现共同积极防疫。

关键词: 演化博弈, 突发公共卫生事件, 演化稳定策略

Abstract:

With the change of human living environment, public health emergencies occur frequently in recent years. The mutual cooperation between the public and local government is an inevitable choice to deal with the public health emergencies timely and efficiently. Based on the assumption of bounded rationality, this paper discusses the evolution process of the behaviors of the public and local governments, and obtains evolutionarily stable strategies under different conditions. MATLAB is applied for simulation and to analyze how the rewards and the punishments to the public from local governments, the punishments to local governments from the superior departments, and other factors influence the public and local government's strategies. The results in this work show that an effectively promoted mutual cooperation between the public and the government and an active epidemic prevention can be achieved by improving relevant subsidy policies, popularizing epidemic-related laws and regulations, increasing the punishment for violating the epidemic-related rules and regulations, and increasing local government penalties for loosening epidemic prevention.

Key words: evolutionary game, public health emergencies, evolutionarily stable strategy

中图分类号:

O225

许智琪, 程郁琨, 姚双良. 突发公共卫生事件中地方政府与社会公众间的演化博弈研究[J]. 运筹学学报（中英文）, 2021, 25(4): 1-14.

Zhiqi XU, Yukun CHENG, Shuangliang YAO. Evolutionary analysis on cooperative behavior of local government and the public in the public health emergencies[J]. Operations Research Transactions, 2021, 25(4): 1-14.

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符号	符号意义	说明
$ C_1 $	地方政府采取严格防控时的成本
$ kC_1 $	地方政府采取宽松防控的成本	$ 0 {\leqslant} k {\leqslant} 1 $
$ U $	社会公众的机会成本
$ V $	公众罚款额
$ Q $	地方政府对公众的补偿、补贴
$ C_2 $	公众随意流动, 地方政府防控成本的增加额
$ R $	公众随意流动的效益
$ C_3 $	公众自觉隔离, 地方政府防控成本的减少额
$ p $	地方政府发现公众随意流动的概率	$ 0{\leqslant} p {\leqslant} 1 $
$ W $	因地方政府防控不得力, 上级部门对其的惩罚
$ d $	地方政府对疫情防控措施的执行力度	$ 0 {\leqslant} d {\leqslant} 1 $

公众	政府
	严格防控策略	宽松防控策略
自觉隔离	$ Q-U $, $ C_3-C_1-Q $	$ Q-U $, $ C_3-kC_1-Q-(1-d)W $
随意流动	$ R-V $, $ V-C_1-C_2 $	$ R-pV + (1-p)Q $, $ pV-(1-p)Q-kC_1-C_2-(1-d)W $

平衡点	$ {\rm det} J $	$ {\rm tr} J $
$ (0, 0) $	$ Z_2Z_3 $	$ Z_2+Z_3 $
$ (0, 1) $	$ - (Z_1 + Z_2)Z_3 $	$ (Z_1 + Z_2) - Z_3 $
$ (1, 0) $	$ - Z_2( - Z_1 + Z_3) $	$ -Z_2 +(-Z_1+Z_3) $
$ (1, 1) $	$ -(Z_1+Z_2)(-1)(-Z_1+Z_3) $	$ -Z_2 +(-Z_1+Z_3) $
$ ({x^ * }, {y^ * }) $	$ -\frac{{Z_2Z_3(Z_1 + Z_2)(Z_1 - Z_3)}}{{Z_1}^2} $	0

均衡点	$ Z_2>0 $
	$ -Z_1+Z_3>0 $			$ -Z_1+Z_3<0<Z_3 $			$ Z_3<0 $
	$ {\rm det} J $	$ {\rm tr} J $	稳定点	$ {\rm det} J $	$ {\rm tr} J $	稳定点	$ {\rm det} J $	$ {\rm tr} J $	稳定点
$ (0, 0) $	+	+	非稳定点	+	+	非稳定点	$ - $	\	鞍点
$ (0, 1) $	$ - $	\	鞍点	–	\	鞍点	+	+	非稳定点
$ (1, 0) $	$ - $	\	鞍点	+	–	ESS	+	–	ESS
$ (1, 1) $	+	–	ESS	–	\	鞍点	–	\	鞍点
$ ({x^ * }, {y^ * }) $	非平衡点			非平衡点			非平衡点

均衡点	$ {Z_2} < 0 < {Z_1} + {Z_2} $
	$ -Z_1+Z_3>0 $	$ -Z_1+Z_3<0<Z_3 $	$ Z_3<0 $
	$ {\rm det} J $	$ {\rm tr} J $	稳定点	$ {\rm det} J $	$ {\rm tr} J $	稳定点	$ {\rm det} J $	$ {\rm tr} J $	稳定点
$ (0, 0) $	–	\	鞍点	–	\	鞍点	+	–	ESS
$ (0, 1) $	–	\	鞍点	–	\	鞍点	+	+	非稳定点
$ (1, 0) $	+	+	非稳定点	–	\	鞍点	–	\	鞍点
$ (1, 1) $	+	–	ESS	–	\	鞍点	–	\	鞍点
$ ({x^ * }, {y^ * }) $	非平衡点			+	0	非稳定点	非平衡点