基于CIS值的双边链路形成策略优化两型博弈方法

doi:10.3969/j.issn.1001-506X.2020.07.17

Abstract

Abstract:

Game theory is a prevailing tool for network formation model and is used widely in the field. The existing research mainly uses the cooperative or non-cooperative game to solve the network formation problem, but such a game approach is not well used to reveal the essence of the problem. The non-cooperative and cooperative biform game method is used to study the strategy optimization problem of the network link formation, which can effectively combine the strategy design in the non-cooperative stage with the benefit distribution in the cooperative stage. Firstly, in the non-cooperative game stage, the strategy is designed and the competitive situations of the 2nd stage is formed. Secondly, in the cooperative game stage, the coalitions and cooperative games are formed based on the competitive situations of the non-cooperative stage in the 1st stage. Moreover, the Semi-CIS value is used to solve the benefit allocation values of the players in each competitive situation. Then, the obtained benefit allocation values are used as the payments of the players in the non-cooperative game stage. The pure strategy Nash equilibrium solution in the non-cooperative stage is obtained, and the optimal solution of the bilateral link formation biform game model is obtained (i.e., link connection). Finally, the validity and usability of the built model are verified by the numerical example, which can provide the theoretical method for studying more complex network formation problems.

Key words: bilateral link, non-cooperative game, cooperative game, biform game, Semi-CIS value

CLC Number:

Xiaoli DU, Kairong LIANG, Dengfeng LI. Biform game approach to strategy optimization of bilateral link formation based on CIS value[J]. Systems Engineering and Electronics, 2020, 42(7): 1550-1557.

Figures/Tables 4

Table 1

Table 2

Value of alliance utility in the strategy situation of 3 players"

局中人策略		局中人1
		0			1			2
		局中人2			局中人2			局中人2
		0	1	2	0	1	2	0	1	2
局中人 3	0	V(1, 2, 3)=6	V(1, 2, 3)=6	V(1, 2, 3)=6	V(1, 2, 3)=6	V(1, 2, 3)=7.6	V(1, 2, 3)=6	V(1, 2, 3)=6	V(1, 2, 3)=6	V(1, 2, 3)=6
		V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4
		V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3
		V(1, 2)=5	V(1, 2)=5	V(1, 2)=5	V(1, 2)=5	V(1, 2)=6.6	V(1, 2)=5	V(1, 2)=5	V(1, 2)=5	V(1, 2)=5
		V (1)=2	V(1)=2	V(1)=2	V (1)=2	V(1)=2	V(1)=2	V (1)=2	V(1)=2	V(1)=2
		V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3
		V (3)=1	V(3)=1	V(3)=1	V (3)=1	V(3)=1	V(3)=1	V (3)=1	V(3)=1	V(3)=1
	1	V(1, 2, 3)=6	V(1, 2, 3)=7.16	V(1, 2, 3)=6	V(1, 2, 3)=6.72	V(1, 2, 3)=15.48	V(1, 2, 3)=6.72	V(1, 2, 3)=6	V(1, 2, 3)=7.16	V(1, 2, 3)=6.91
		V(2, 3)=4	V(2, 3)=5.16	V(2, 3)=4	V(2, 3)=4	V(2, 3)=5.16	V(2, 3)=4	V(2, 3)=4	V(2, 3)=5.16	V(2, 3)=4
		V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3.72	V(1, 3)=3.72	V(1, 3)=3.72	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3
		V(1, 2)=5	V(1, 2)=5	V(1, 2)=5	V(1, 2)=5	V(1, 2)=6.6	V(1, 2)=5	V(1, 2)=5	V(1, 2)=5	V(1, 2)=5
		V (1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2
		V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3
		V (3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1
	1	V(1, 2, 3)=6	V(1, 2, 3)=6	V(1, 2, 3)=6	V(1, 2, 3)=6	V(1, 2, 3)=7.6	V(1, 2, 3)=6.73	V(1, 2, 3)=6	V(1, 2, 3)=6.54	V(1, 2, 3)=6
		V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4	V(2, 3)=4
		V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3	V(1, 3)=3
		V(1, 2)=5	V(1, 2)=5	V(1, 2)=5	V(1, 2)=5	V(1, 2)=6.6	V(1, 2)=5	V(1, 2)=5	V(1, 2)=5	V(1, 2)=5
		V (1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2	V(1)=2
		V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3	V(2)=3
		V (3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1	V(3)=1

Table 2

Table 3

Table 4

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局中人策略		局中人1
		0			1			2
		局中人2			局中人2			局中人2
		0	1	2	0	1	2	0	1	2
局中人 3	0	S₁=(0, 0, 0)	S₂=(0, 1, 0)	S₃=(0, 2, 0)	S₄=(1, 0, 0)	S₅=(1, 1, 0)	S₆=(1, 2, 0)	S₇=(2, 0, 0)	S₈=(2, 1, 0)	S₉=(2, 2, 0)
	1	S₁₀=(0, 0, 1)	S₁₁=(0, 1, 1)	S₁₂=(0, 2, 1)	S₁₃=(1, 0, 1)	S₁₄=(1, 1, 1}	S₁₅=(1, 2, 1)	S₁₆=(2, 0, 1)	S₁₇=(2, 1, 1)	S₁₈=(2, 2, 1)
	2	S₁₉=(0, 0, 2)	S₂₀=(0, 1, 2)	S₂₁=(0, 2, 2)	S₂₂=(1, 0, 2)	S₂₃=(1, 1, 2)	S₂₄=(1, 2, 2)	S₂₅=(2, 0, 2)	S₂₆=(2, 1, 2)	S₂₇=(2, 2, 2)

局中人策略		局中人1
		0			1			2
		局中人2			局中人2			局中人2
		0	1	2	0	1	2	0	1	2
局中人3	0	2.53	2.53	2.53	2.53	3.07	2.53	2.53	2.53	2.53
		4.40	4.40	4.40	4.40	4.93	4.40	4.40	4.40	4.40
		0.67	0.67	0.67	0.67	1.20	0.67	0.67	0.67	0.67
	1	2.53	2.92	2.53	2.77	5.69	2.77	2.53	2.92	2.84
		4.40	4.79	4.40	4.64	7.56	4.64	4.40	4.79	4.70
		0.67	1.05	0.67	0.91	3.83	0.91	0.67	1.05	0.97
	2	2.53	2.53	2.53	2.53	3.07	2.77	2.53	2.71	2.53
		4.40	4.40	4.40	4.40	4.93	4.64	4.40	4.58	4.40
		0.67	0.67	0.67	0.67	1.20	0.91	0.67	0.85	0.67

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Biform game approach to strategy optimization of bilateral link formation based on CIS value

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局中人策略		局中人1
		0			1			2
		局中人2			局中人2			局中人2
		0	1	2	0	1	2	0	1	2
局中人3	0	7.6	7.6	7.6	7.6	9.2	7.6	7.6	7.6	7.6
	1	7.6	8.76	7.6	8.32	17.08	8.32	7.6	8.76	7.6
	2	7.6	7.6	7.6	7.6	9.2	8.32	7.6	8.14	7.6