基于Bayesian Stackelberg多阶段博弈的网络信息体系方案优选

doi:10.3969/j.issn.1001-506X.2020.06.13

系统工程与电子技术 ›› 2020, Vol. 42 ›› Issue (6): 1301-1309.doi: 10.3969/j.issn.1001-506X.2020.06.13

基于Bayesian Stackelberg多阶段博弈的网络信息体系方案优选

禹明刚^1,²(), 何明¹(), 张东戈^1,*(), 贾连祥³()

1. 陆军工程大学指挥控制工程学院, 江苏南京 210007
2. 陆军工程大学通信工程学院, 江苏南京 210007
3. 中国人民解放军32142部队, 河北保定 071000

收稿日期:2019-07-28 出版日期:2020-06-01 发布日期:2020-06-01
通讯作者: 张东戈 E-mail:yuminggang8989@163.com;heming@126.com;329674406@qq.com;jialianxiang001@163.com
作者简介:禹明刚(1986-),男,讲师,博士,主要研究方向为军事需求工程、体系工程。E-mail:yuminggang8989@163.com|何明(1978-),男,教授,博士,主要研究方向为军事对抗仿真、演化博弈。E-mail:heming@126.com|贾连祥(1981-),男,工程师,硕士,主要研究方向为系统工程。E-mail:jialianxiang001@163.com
基金资助:
国家自然科学基金青年科学基金项目(71901217);国家重点研发计划(2018YFC0806900)

Scheme optimization for network information-centric system-of-systems based on multi-stage Bayesian Stackelberg game

Minggang YU^1,²(), Ming HE¹(), Dongge ZHANG^1,*(), Lianxiang JIA³()

1. Institute of Command and Control Engineering, Army Engineering University of PLA, Nanjing 210007, China
2. Institute of Communication Engineering, Army Engineering University of PLA, Nanjing 210007, China
3. Unit 32142 of the PLA, Baoding 071000, China

Received:2019-07-28 Online:2020-06-01 Published:2020-06-01
Contact: Dongge ZHANG E-mail:yuminggang8989@163.com;heming@126.com;329674406@qq.com;jialianxiang001@163.com
Supported by:
国家自然科学基金青年科学基金项目(71901217);国家重点研发计划(2018YFC0806900)

摘要/Abstract

摘要：

针对对抗及不确定环境下的网络信息体系建设方案优选问题,考虑经典博弈论中理性和共同知识假设失效的局限,提出了基于Bayesian Stackelberg的多阶段博弈模型。首先分析网络信息体系建设方案优选需求,给出3个基本假设;在此基础上,构建反映各阶段参与人信念的博弈子情景,集结子情景形成全时域情景,并分别给出情景的策略集及支付函数;分析全时域情景的纳什均衡,预测对手可能的均衡策略;最后,集结全时域情景形成全局情景,在风险可控范围内选择全局情景中期望支付较大策略,作为较优体系方案。通过算例分析检验了该方法中己方最坏选择是“综合均衡策略”,且在风险可控范围内最终策略将严格优于该策略。

关键词: 网络信息体系, Stackelberg, 多阶段博弈, 有限理性, 方案优选

Abstract:

In order to solve the problem of scheme optimization for network information-centric system-of-systems (NICSoS) in military conflict and uncertainty environments, a multi-stage game method based on Bayesian Stackelberg is proposed considering the limitation of the failure of rationality and common hypothesis in classical game theory. It starts with the requirement analysis of NICSoS construction scheme optimization, and three basic assumptions are given. Then the sub-scenarios which reflects participants' beliefs at different stages and the full-time domain scenarios are constructed. Furthermore, strategy sets and payment functions are given. The Nash equilibrium of full-time domain scenarios is analyzed to predict the possible equilibrium strategy of the opponent. Finally, the full-time domain scenarios are aggregated into global scenarios, and the strategies with higher expected payment in the global scenarios are selected within the scope of controllable risks. Case study shows the strategy that generated by this method is no worse than comprehensive equilibrium and can be exactly better than it within the scope of controllable risk.

Key words: network information-centric system-of-systems, Stackelberg, multi-stage game, bounded rationality, scheme optimization

中图分类号:

TP391

禹明刚, 何明, 张东戈, 贾连祥. 基于Bayesian Stackelberg多阶段博弈的网络信息体系方案优选[J]. 系统工程与电子技术, 2020, 42(6): 1301-1309.

Minggang YU, Ming HE, Dongge ZHANG, Lianxiang JIA. Scheme optimization for network information-centric system-of-systems based on multi-stage Bayesian Stackelberg game[J]. Systems Engineering and Electronics, 2020, 42(6): 1301-1309.

图/表 11

图1

表1

表2

表3

表4

表5

表6

表7

表8

全时域情景G4收益矩阵"

	(E′, M′)	(E′, L′)	(E′, R′)	(E′, V′)	(E′, I′)	(H′, M′)	(H′, L′)
(E, M)	(0.70, 0.67)	(0.66, -0.62)	(0.67, 0.14)	(0.69, 0.50)	(0.69, 0.60)	(0.70, 0.69)	(0.70, -0.11)
(E, L)	(0.46, 0.65)	(0.45, -0.60)	(0.46, 0.13)	(0.44, 0.50)	(0.43, 0.63)	(0.44, 0.70)	(0.40, -0.12)
(E, R)	(-0.20, 0.65)	(-0.21, -0.60)	(-0.19, 0.12)	(-0.20, 0.48)	(-0.22, 0.63)	(-0.18, 0.77)	(-0.20, -0.10)
(E, V)	(0.15, 0.67)	(0.16, -0.62)	(0.15, 0.12)	(0.17, 0.50)	(0.17, 0.62)	(0.14, 0.79)	(0.15, -0.10)
(E, I)	(0.10, 0.67)	(0.11, -0.62)	(0.09, 0.13)	(0.10, 0.50)	(0.12, 0.62)	(0.11, 0.77)	(0.10, -0.10)
(H, M)	(-0.20, 0.66)	(-0.25, -0.62)	(-0.25, 0.13)	(-0.21, 0.49)	(-0.20, 0.64)	(-0.28, 0.77)	(-0.29, -0.11)
(H, L)	(0.25, 0.67)	(0.24, -0.61)	(0.22, 0.15)	(0.25, 0.50)	(0.26, 0.63)	(0.25, 0.76)	(0.23, -0.10)
(H, R)	(-0.10, 0.64)	(-0.09, -0.63)	(-0.11, 0.13)	(-0.11, 0.48)	(-0.12, 0.63)	(-0.11, 0.75)	(-0.10, -0.12)
(H, V)	(-0.15, 0.67)	(-0.13, -0.62)	(-0.13, 0.13)	(-0.16, 0.48)	(-0.18, 0.64)	(-0.17, 0.79)	(-0.17, -0.10)
(B, M)	(0.00, 0.65)	(0.00, -0.63)	(0.00, 0.14)	(0.00, 0.50)	(0.00, 0.63)	(0.00, 0.75)	(0.00, -0.11)
(B, L)	(0.58, 0.64)	(0.56, -0.62)	(0.56, 0.14)	(0.56, 0.50)	(0.57, 0.60)	(0.57, 0.76)	(0.57, -0.12)
(B, R)	(-0.06, 0.65)	(-0.05, -0.61)	(-0.06, 0.13)	(-0.05, 0.51)	(-0.06, 0.60)	(-0.06, 0.74)	(-0.07, -0.10)
(B, V)	(0.40, 0.67)	(0.38, -0.63)	(0.38, 0.13)	(0.40, 0.50)	(0.40, 0.63)	(0.39, 0.78)	(0.40, -0.12)
(B, I)	(0.66, 0.66)	(0.65, -0.62)	(0.65, 0.14)	(0.64, 0.51)	(0.64, 0.61)	(0.67, 0.79)	(0.66, -0.10)
	(H′, R′)	(H′, V′)	(H′, I′)	(B′, M′)	(B′, L′)	(B′, R′)	(B′, I′)
(E, M)	(0.65, -0.14)	(0.65, -0.18)	(0.67, 0.42)	(0.65, 0.75)	(0.64, -0.49)	(0.70, 0.65)	(0.67, 0.13)
(E, L)	(0.43, -0.15)	(0.46, -0.20)	(0.41, 0.42)	(0.41, 0.70)	(0.42, -0.48)	(0.45, 0.65)	(0.45, 0.13)
(E, R)	(-0.22, -0.16)	(-0.19, -0.18)	(-0.18, 0.43)	(-0.20, 0.70)	(-0.18, -0.50)	(-0.19, 0.65)	(-0.21, 0.16)
(E, V)	(0.14, -0.15)	(0.14, -0.18)	(0.16, 0.43)	(0.17, 0.75)	(0.15, -0.52)	(0.14, 0.64)	(0.14, 0.15)
(E, I)	(0.11, -0.13)	(0.12, -0.20)	(0.12, 0.40)	(0.10, 0.75)	(0.12, -0.50)	(0.11, 0.60)	(0.10, 0.15)
(H, M)	(-0.27, -0.15)	(-0.27, -0.22)	(-0.27, 0.40)	(-0.28, 0.71)	(-0.26, -0.51)	(-0.21, 0.67)	(-0.21, 0.16)
(H, L)	(0.23, -0.14)	(0.23, -0.23)	(0.24, 0.43)	(0.21, 0.72)	(0.22, -0.51)	(0.22, 0.68)	(0.25, 0.15)
(H, R)	(-0.12, -0.13)	(-0.09, -0.22)	(-0.11, 0.44)	(-0.09, 0.74)	(-0.12, -0.53)	(-0.10, 0.66)	(-0.10, 0.13)
(H, V)	(-0.15, -0.15)	(-0.15, -0.22)	(-0.16, 0.43)	(-0.13, 0.75)	(-0.13, -0.50)	(-0.15, 0.60)	(-0.14, 0.15)
(B, M)	(0.00, -0.13)	(0.00, -0.20)	(0.00, 0.40)	(0.00, 0.74)	(0.00, -0.53)	(0.00, 0.65)	(0.00, 0.14)
(B, L)	(0.55, -0.15)	(0.56, -0.19)	(0.56, 0.42)	(0.56, 0.75)	(0.57, -0.50)	(0.58, 0.65)	(0.55, 0.14)
(B, R)	(-0.05, -0.13)	(-0.07, -0.20)	(-0.06, 0.43)	(-0.05, 0.71)	(-0.06, -0.52)	(-0.07, 0.60)	(-0.05, 0.15)
(B, V)	(0.41, -0.15)	(0.40, -0.19)	(0.41, 0.44)	(0.40, 0.73)	(0.39, -0.52)	(0.39, 0.64)	(0.40, 0.15)
(B, I)	(0.66, -0.13)	(0.65, -0.20)	(0.66, 0.43)	(0.64, 0.75)	(0.64, -0.50)	(0.67, 0.66)	(0.67, 0.14)

表8

表9

全局情景G收益矩阵"

	(E′, M′)	(E′, L′)	(E′, R′)	(E′, V′)	(E′, I′)	(H′, M′)	(H′, L′)
(E, M)	(0.71, 0.66)	(0.68, -0.77)	(0.68, 0.14)	(0.70, 0.25)	(0.69, 0.56)	(0.71, 0.74)	(0.70, -0.13)
(E, L)	(0.46, 0.63)	(0.44, -0.80)	(0.44, 0.15)	(0.44, 0.50)	(0.43, 0.63)	(0.44, 0.70)	(0.40, -0.12)
(E, R)	(-0.23, 0.63)	(-0.21, -0.74)	(-0.19, 0.12)	(-0.20, 0.48)	(-0.22, 0.63)	(-0.18, 0.77)	(-0.20, -0.10)
(E, V)	(0.24, 0.67)	(0.16, -0.62)	(0.15, 0.12)	(0.17, 0.50)	(0.17, 0.62)	(0.14, 0.79)	(0.15, -0.10)
(E, I)	(0.01, 0.66)	(0.11, -0.62)	(0.09, 0.13)	(0.10, 0.50)	(0.12, 0.62)	(0.11, 0.77)	(0.10, -0.10)
(H, M)	(-0.37, 0.65)	(-0.25, -0.62)	(-0.25, 0.13)	(-0.21, 0.49)	(-0.20, 0.64)	(-0.28, 0.77)	(-0.29, -0.11)
(H, L)	(0.25, 0.64)	(0.24, -0.61)	(0.22, 0.15)	(0.25, 0.50)	(0.26, 0.63)	(0.25, 0.76)	(0.23, -0.10)
(H, R)	(-0.09, 0.64)	(-0.09, -0.63)	(-0.11, 0.13)	(-0.11, 0.48)	(-0.12, 0.63)	(-0.11, 0.75)	(-0.10, -0.12)
(H, V)	(0.22, 0.66)	(-0.13, -0.62)	(-0.13, 0.13)	(-0.16, 0.48)	(-0.18, 0.64)	(-0.17, 0.79)	(-0.17, -0.10)
(B, M)	(0.00, 0.65)	(0.00, -0.63)	(0.00, 0.14)	(0.00, 0.50)	(0.00, 0.63)	(0.00, 0.75)	(0.00, -0.11)
(B, L)	(0.58, 0.64)	(0.56, -0.62)	(0.56, 0.14)	(0.56, 0.50)	(0.57, 0.60)	(0.57, 0.76)	(0.57, -0.12)
(B, R)	(-0.06, 0.65)	(-0.05, -0.61)	(-0.06, 0.13)	(-0.05, 0.51)	(-0.06, 0.60)	(-0.06, 0.74)	(-0.07, -0.10)
(B, V)	(0.40, 0.67)	(0.38, -0.63)	(0.38, 0.13)	(0.40, 0.50)	(0.40, 0.63)	(0.39, 0.78)	(0.40, -0.12)
(B, I)	(0.66, 0.66)	(0.65, -0.62)	(0.65, 0.14)	(0.64, 0.51)	(0.64, 0.61)	(0.67, 0.79)	(0.66, -0.10)
	(H′, R′)	(H′, V′)	(H′, I′)	(B′, M′)	(B′, L′)	(B′, R′)	(B′, I′)
(E, M)	(0.67, -0.14)	(0.68, -0.02)	(0.69, 0.60)	(0.65, 0.75)	(0.60, -0.49)	(0.70, 0.65)	(0.67, 0.13)
(E, L)	(0.43, -0.15)	(0.46, -0.20)	(0.41, 0.42)	(0.41, 0.70)	(0.42, -0.48)	(0.45, 0.65)	(0.45, 0.13)
(E, R)	(-0.22, -0.16)	(-0.19, -0.18)	(-0.18, 0.43)	(-0.20, 0.70)	(-0.18, -0.50)	(-0.19, 0.65)	(-0.21, 0.16)
(E, V)	(0.14, -0.15)	(0.14, -0.18)	(0.16, 0.43)	(0.17, 0.75)	(0.15, -0.52)	(0.14, 0.64)	(0.14, 0.15)
(E, I)	(0.11, -0.13)	(0.12, -0.20)	(0.12, 0.40)	(0.10, 0.75)	(0.12, -0.50)	(0.11, 0.60)	(0.10, 0.15)
(H, M)	(-0.27, -0.15)	(-0.27, -0.22)	(-0.27, 0.40)	(-0.28, 0.71)	(-0.26, -0.51)	(-0.21, 0.67)	(-0.21, 0.16)
(H, L)	(0.23, -0.14)	(0.23, -0.23)	(0.24, 0.43)	(0.21, 0.72)	(0.22, -0.51)	(0.22, 0.68)	(0.25, 0.15)
(H, R)	(-0.12, -0.13)	(-0.09, -0.22)	(-0.11, 0.44)	(-0.09, 0.74)	(-0.12, -0.53)	(-0.10, 0.66)	(-0.10, 0.13)
(H, V)	(-0.15, -0.15)	(-0.15, -0.22)	(-0.16, 0.43)	(-0.13, 0.75)	(-0.13, -0.50)	(-0.15, 0.60)	(-0.14, 0.15)
(B, M)	(0.00, -0.13)	(0.00, -0.20)	(0.00, 0.40)	(0.00, 0.74)	(0.00, -0.53)	(0.00, 0.65)	(0.00, 0.14)
(B, L)	(0.55, -0.15)	(0.56, -0.19)	(0.56, 0.42)	(0.56, 0.75)	(0.57, -0.50)	(0.58, 0.65)	(0.55, 0.14)
(B, R)	(-0.05, -0.13)	(-0.07, -0.20)	(-0.06, 0.43)	(-0.05, 0.71)	(-0.06, -0.52)	(-0.07, 0.60)	(-0.05, 0.15)
(B, V)	(0.41, -0.15)	(0.40, -0.19)	(0.41, 0.44)	(0.40, 0.73)	(0.39, -0.52)	(0.39, 0.64)	(0.40, 0.15)
(B, I)	(0.66, -0.13)	(0.65, -0.20)	(0.66, 0.43)	(0.64, 0.75)	(0.64, -0.50)	(0.67, 0.66)	(0.67, 0.14)

表9

表10

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	E′	H′
E	(0.80, 0.75)	(0.80, 0.63)
H	(0.50, 0.75)	(0.50, 0.63)

	E′	H′	B′
E	(0.80, 0.75)	(0.80, 0.63)	(0.80, 0.62)
H	(0.50, 0.75)	(0.50, 0.63)	(0.50, 0.62)
B	(0.91, 0.75)	(0.91, 0.63)	(0.91, 0.62)

	M′	L′	R′
M	(0.43, 0.71)	(0.43, 0.51)	(0.43, 0.77)
L	(0.30, 0.71)	(0.30, 0.51)	(0.30, 0.77)
R	(0.90, 0.71)	(0.90, 0.51)	(0.90, 0.77)

	M′	L′	R′	V′	I′
M	(0.43, 0.71)	(0.43, 0.51)	(0.43, 0.77)	(0.43, 0.67)	(0.43, 0.81)
L	(0.30, 0.71)	(0.30, 0.51)	(0.30, 0.77)	(0.30, 0.67)	(0.30, 0.81)
R	(0.90, 0.71)	(0.90, 0.51)	(0.90, 0.77)	(0.90, 0.67)	(0.90, 0.81)
V	(0.64, 0.71)	(0.64, 0.51)	(0.64, 0.77)	(0.64, 0.67)	(0.64, 0.81)
I	(0.85, 0.71)	(0.85, 0.51)	(0.85, 0.77)	(0.85, 0.67)	(0.85, 0.81)

	(E′, M′)	(E′, L′)	(E′, R′)	(H′, M′)	(H′, L′)	(H′, R′)
(E, M)	(0.73, 0.65)	(0.70, -1.00)	(0.70, 0.15)	(0.73, 0.82)	(0.69, -0.15)	(0.70, -0.14)
(E, L)	(0.45, 0.59)	(0.43, -1.10)	(0.42, 0.17)	(0.46, 0.80)	(0.45, -0.16)	(0.41, -0.12)
(E, R)	(-0.27, 0.61)	(-0.20, -0.95)	(-0.25, 0.15)	(-0.25, 0.82)	(-0.23, -0.16)	(-0.26, -0.16)
(H, M)	(-0.63, 0.63)	(-0.61, -0.96)	(-0.61, 0.16)	(-0.63, 0.81)	(-0.64, -0.14)	(-0.70, -0.12)
(H, L)	(0.24, 0.60)	(0.25, -1.00)	(0.27, 0.13)	(0.22, 0.80)	(0.22, -0.13)	(0.23, -0.13)
(H, R)	(-0.08, 0.64)	(-0.07, -1.20)	(-0.06, 0.14)	(-0.08, 0.79)	(-0.06, -0.15)	(-0.07, -0.15)

基于Bayesian Stackelberg多阶段博弈的网络信息体系方案优选

Scheme optimization for network information-centric system-of-systems based on multi-stage Bayesian Stackelberg game

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G^m	纳什均衡		期望支付 ${\rm{E}}[{\Psi _R}(\overline {N_R^m}, \overline {N_B^m})]$
G^m	$\overline {N_R^m} $	$\overline {N_B^m} $
G¹	(E, M)	(H′, M′)	0.73
G²	(0.4(E, M), 0.3(E, V), 0.3(H, V))	(0.7(H′, M′), 0.3(H′, I′))	0.65
G³	(E′, M′)	(B′, R′)	0.70
G⁴	(0.6(E, M), 0.4(H, L))	(0.2(E′, M′), 0.5(B′, M′), 0.3(B′, R′))	0.49
	综合均衡		综合期望支付 ${\rm{E}}[{\Psi _R}(\hat R, \hat B)]$
	${\hat R}$	${\hat B}$	综合期望支付 ${\rm{E}}[{\Psi _R}(\hat R, \hat B)]$
	(0.76(E, M), 0.06(E, V), 0.06(H, V), 0.12(H, L))	(0.06(E′, M′), 0.34(H′, M′), 0.06(H′, I′), 0.15(B′, M′), 0.39(B′, R′))	0.63

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