基于一致性的联盟Banzhaf值的刻画及其在产业联盟创新收益分配中的应用

doi:10.16381/j.cnki.issn1003-207x.2023.1370

Abstract

Abstract:

Industry alliances serve as a potent conduit for enhancing innovation outputs among firms. However， the dissolution of such alliances is frequently precipitated by inequitable innovation revenue distribution mechanisms. The phenomenon of re-alliance among enterprises within an industry alliance is addressed， and the cooperative game with coalition structure is introduced to delineate the existence of preferential alliances among enterprises. Subsequently， the classic axiom of consistency is extended to cooperative games with coalition structures， axiomatizing the Banzhaf value with coalition structure within this framework. The consistency axiom underscores the intrinsic stability of allocation rules， stipulating that when a subset of participants departs with their allocated gains， the remaining participants’ shares in the resultant reduced game should align with their shares in the original game. Consequently， an allocation rule that satisfies the consistency ensures that agreements formulated under this rule remain unaltered irrespective of participant count fluctuations. Then， a three-stage extended game model is constructed for the distribution of innovation revenues within industry alliances， examining the operational mechanism of the Banzhaf value with coalition structure. Finally， three novel innovation revenue distribution schemes are proposed， predicated on the Banzhaf value with coalition structure， and an empirical analysis is conducted using the intelligent voice intellectual property industry alliance as a case study.The findings indicate　（1） The Banzhaf value with coalition structure possess inherent stability and is uniquely characterized by consistency within the priori union and standardization. （2） Within the three-stage extended game model for the distribution of innovation revenues in industry alliances， the Banzhaf value with coalition structure constitutes the subgame perfect equilibrium for the initial two stages. （3） Scheme one， predicated on the Banzhaf value with coalition structure， not only fosters the development of dominant enterprises but also safeguards the stability of the industry alliance. Scheme two enhances solidarity among enterprises within the industry alliance， facilitating the flow of innovation elements. Scheme three is more apt for industry alliances constituted by risk-neutral enterprises.

Key words: cooperative games, priori union, Banzhaf value, consistency, industry alliance

CLC Number:

F224.32

Wenrong Lv,Erfang Shan,Tao Liu, et al. Consistency of the Banzhaf Value with Coalition Structure and Its Application in Innovation Benefit Allocation of the Industrial Alliance[J]. Chinese Journal of Management Science, 2026, 34(5): 86-96.

Figures/Tables 5

References 28

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企业	R&D经费投入	产出系数	成本系数
1	22	9	0.35
2	9	12	0.24
3	16	3	0.17
4	19	6	0.36
5	2	5	0.65
6	12	10	0.53

序号	联盟Banzhaf值	方案1	方案2	方案3	Shapley值	Banzhaf值	Owen值
1	44031.129	55396.622	52332.129	50256.879	76543.700	79154.816	77195.113
2	25122.701	31607.473	33423.701	37574.201	37972.680	38690.421	36876.030
3	26888.579	33829.168	35189.579	33114.329	24796.640	24870.881	24950.240
4	26042.556	32764.765	34343.556	38494.05	39788.220	40597.536	38602.770
5	43912.871	55247.838	52213.871	50138.621	21871.875	21803.184	23497.763
6	26955.919	33913.889	35256.919	33181.669	41786.640	42692.481	41637.840
总和	192953.755	242759.755	242759.755	242759.755	242759.755	247809.319	242759.755

Consistency of the Banzhaf Value with Coalition Structure and Its Application in Innovation Benefit Allocation of the Industrial Alliance

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