基于改进复制动态演化博弈模型的最优防御策略选取

doi:10.11959/j.issn.1000-436x.2018010

Abstract

Abstract:

In terms of the existence of strategy dependency in the same game group,network attack-defense evolutionary game model based on the improved replicator dynamics was constricted by introducing the intensity coefficient,which completed the method of calculating replicator dynamic rate.The improved replicator dynamic equation was adopted to solve the evolutionary equilibrium for the situation that both attack and defense have two optional strategies.The stability of the equilibrium points was analyzed by the local stability analysis method of Jacobian matrix,and the optimal defense strategies were obtained under different conditions.The results show that the strategy dependency between the players in the same group has a certain influence on the evolution of the game,both the incentive and the inhibition.Finally,the accuracy and validity of the model and method are verified by the experimental simulation,which provides a new theoretical support for solving the information security problems in the real.

Key words: strategy dependency, strength coefficient, improving replicator dynamic, replicator dynamic rate, Jacobian matrix, optimal defense strategy

CLC Number:

TP390

Jianming HUANG,Hengwei ZHANG. Improving replicator dynamic evolutionary game model for selecting optimal defense strategies[J]. Journal on Communications, 2018, 39(1): 170-182.

Figures/Tables 23

均衡点(q₁,p₁)	$J$ 的行列式和迹的计算式
A (0,0)	$\det J = α_{1} β_{1} (d_{21} - λ_{21} d_{22}) (a_{12} - γ_{21} a_{22})$
	$tr J = α_{1} (d_{21} - λ_{21} d_{22}) + β_{1} (a_{12} - γ_{21} a_{22})$
B (0,1)	$\det J = - α_{1} β_{1} (d_{11} - λ_{21} d_{12}) (a_{12} - γ_{21} a_{22})$
	$tr J = α_{1} (d_{11} - λ_{21} d_{12}) - β_{1} (a_{12} - γ_{21} a_{22})$
C (1,0)	$\det J = - α_{1} β_{1} (d_{21} - λ_{21} d_{22}) (a_{11} - γ_{21} a_{21})$
	$tr J = - α_{1} (d_{21} - λ_{21} d_{22}) + β_{1} (a_{11} - γ_{21} a_{21})$
D (1,1)	$\det J = α_{1} β_{1} (d_{11} - λ_{21} d_{12}) (a_{11} - γ_{21} a_{21})$
	$tr J = - α_{1} (d_{11} - λ_{21} d_{12}) - β_{1} (a_{11} - γ_{21} a_{21})$

情形	判别依据	A(0,0)	B(0,1)	C(1,0)	D(1,1)
	$\det J$	+	–	–	+
情形1	$tr J$	–	不定	不定	+
	稳定性	ESS	鞍点	鞍点	不稳定
	$\det J$	–	+	+	–
情形2	$tr J$	不定	–	+	不定
	稳定性	鞍点	ESS	不稳定	鞍点
	$\det J$	–	+	+	–
情形3	$tr J$	不定	+	–	不定
	稳定性	鞍点	不稳定	ESS	鞍点
	$\det J$	+	–	–	+
情形4	$tr J$	+	不定	不定	–
	稳定性	不稳定	鞍点	鞍点	ESS

情形	判别依据	A(0,0)	B(0,1)	C(1,0)	D(1,1)
	$\det J$	+	–	–	+
情形1	$tr J$	–	不定	不定	+
	稳定性	ESS	鞍点	鞍点	不稳定
	$\det J$	+	–	–	–
情形2	$tr J$	–	不定	+	不定
	稳定性	ESS	鞍点	鞍点	鞍点
	$\det J$	–	+	+	–
情形3	$tr J$	不定	+	–	不定
	稳定性	鞍点	不稳定	ESS	鞍点
	$\det J$	–	+	–	+
情形4	$tr J$	不定	+	不定	–
	稳定性	鞍点	不稳定	鞍点	ESS
	$\det J$	+	+	–	+
情形5	$tr J$	不定	–	不定	+
	稳定性	不定	ESS	鞍点	不稳定
	$\det J$	–	+	+	–
情形6	$tr J$	不定	–	+	不定
	稳定性	鞍点	ESS	不稳定	鞍点
	$\det J$	+	–	+	–
情形7	$tr J$	+	不定	–	不定
	稳定性	不稳定	鞍点	ESS	鞍点
	$\det J$	+	–	–	+
情形8	$tr J$	+	不定	不定	–
	稳定性	不稳定	鞍点	鞍点	ESS

情形	判别依据	A(0,0)	B(0,1)	C(1,0)	D(1,1)
	$\det J$	+	–	–	+
情形1	$tr J$	–	不定	不定	+
	稳定性	ESS	鞍点	鞍点	不稳定
	$\det J$	–	+	+	–
情形2	$tr J$	不定	–	+	不定
	稳定性	鞍点	ESS	不稳定	鞍点
	$\det J$	+	+	–	–
情形3	$tr J$	–	+	不定	不定
	稳定性	ESS	不稳定	鞍点	鞍点
	$\det J$	–	–	+	+
情形4	$tr J$	不定	不定	+	–
	稳定性	鞍点	鞍点	不稳定	ESS
	$\det J$	–	–	+	+
情形5	$tr J$	不定	不定	–	+
	稳定性	鞍点	鞍点	ESS	不稳定
	$\det J$	+	+	–	–
情形6	$tr J$	+	–	不定	不定
	稳定性	不稳定	ESS	鞍点	鞍点
	$\det J$	–	+	+	–
情形7	$tr J$	不定	+	–	不定
	稳定性	鞍点	不稳定	ESS	鞍点
	$\det J$	+	–	–	+
情形8	$tr J$	+	不定	不定	–
	稳定性	不稳定	鞍点	鞍点	ESS

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方法	博弈类型	行为理性	复制动态速率准确性	均衡求解	具体应用
文献[13]方法	随机博弈	完全理性	—	简单	策略选取
文献[14]方法	动态博弈	完全理性	—	一般	策略选取
文献[18]方法	演化博弈	不完全理性	低（未考虑同类策略间的影响）	一般	安全防御
文献[19]方法	演化博弈	不完全理性	低（未考虑同类策略间的影响）	简单	安全防御
本文方法	演化博弈	不完全理性	高（综合考虑并定量描述同类策略间的影响）	详细	策略选取

序号	原子攻击动作名称	网络攻击策略
序号	原子攻击动作名称	AS ₁	AS ₂
a₁	安装Web监听	√
a₂	远程攻击	√
a₃	盗取账户		√
a₄	SSH攻击
a₅	网页攻击	√
a₆	数据库监听		√

序号	原子防御动作名称	网络防御策略
序号	原子防御动作名称	DS ₁	DS ₂
d₁	安装数据库补丁		√
d₂	重装监听程序	√	√
d₃	限制数据分组	√
d₄	删除可疑账户
d₅	重启数据服务器	√	√
d₆	主页修复	√

Improving replicator dynamic evolutionary game model for selecting optimal defense strategies

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Figures/Tables 23

References 31

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