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

摘要/Abstract

摘要：

博弈论作为网络形成模型求解的主流工具,在该领域得到了广泛应用,但现有研究主要采用合作或非合作的单一博弈论方法对网络形成问题进行求解,未能很好地反映问题实质。对此,采用非合作-合作两型博弈方法,研究网络链路形成的策略优化问题,可以有效地结合非合作阶段的策略设计与合作阶段的联盟收益分配。首先,在非合作博弈阶段,进行策略设计并形成第二阶段合作博弈的竞争局势。其次,在合作博弈阶段,基于第一阶段非合作博弈的竞争局势,形成联盟及其合作博弈,并采用Semi-CIS值求解各个竞争局势下合作博弈的局中人(节点)分配值。然后,将得到的分配值作为第一阶段非合作博弈的局中人支付值,计算非合作博弈的纯策略纳什均衡解,进而得到双边链路形成的两型博弈模型的最优解(链路连接)。最后,通过数值实例验证了所建模型与方法的有效性和可用性，为研究更加复杂的网络形成问题提供了理论方法。

关键词: 双边链路, 非合作博弈, 合作博弈, 两型博弈, Semi-CIS值

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

中图分类号:

杜晓丽, 梁开荣, 李登峰. 基于CIS值的双边链路形成策略优化两型博弈方法[J]. 系统工程与电子技术, 2020, 42(7): 1550-1557.

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.

图/表 4

表1

表2

3个局中人策略局势下的联盟效用值"

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

表2

表3

表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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