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

Abstract

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

CLC Number:

TP391

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.

Figures/Tables 11

Fig.1

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Full-time domain scenario G4 profit matrix"

	(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)

Table 8

Table 9

Global scenario G profit matrix"

	(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)

Table 9

Table 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)

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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