基于动态非合作博弈超效率DEA的成本补偿激励方法研究

doi:10.16381/j.cnki.issn1003-207x.2022.1859

Abstract

Abstract:

In practice， a common problem faced by managers is how to motivate decision-making units （DMU） to improve their performance by means of cost compensation. It is especially common in the problems of cost supervision and price mechanism in the monopoly industry and public welfare service industry. The existing cost compensation studies do not provide sufficient positive incentives for effect DMUs， and also do not consider the non-cooperative game relationship that often occurs among DMUs in the face of interests. Therefore， dynamic non-cooperative game is combined with super-efficiency data envelopment analysis （DEA） and a dynamic game super-efficiency DEA algorithm with bidirectional incentive effect is proposed. The convergence of the algorithm is proved and the optimal solution is a unique Nash equilibrium point. The proposed method is applied to 25 provincial-level power grid enterprises of a power grid group in China from 2016 to 2019， and the effectiveness of the method is verified. The results of the case study show that： 1） The operating efficiency of power grid enterprises in different regions is significantly different， and the motivation of performance improvement is not strong； 2） The proposed cost compensation scheme can generate positive or negative incentives for DMU with different performance， and the proposed method is helpful to strengthen the motivation of DMUs to actively improve their performance.It further enriches the DEA theoretical research of cost compensation for incentives and provides an effective management tool for relevant managers in this study.

Key words: cost compensation, non-cooperative game, data envelopment analysis, incentive, performance improvement

CLC Number:

C934

Qian-zhi DAI,Xiao-chi XU,Xi-yang LEI,Qian ZHAO. Cost Compensation Method for Incentives Based on Dynamic Non-cooperative Game and Super-efficiency DEA[J]. Chinese Journal of Management Science, 2023, 31(12): 185-192.

Figures/Tables 5

DMU	$c j$	$b p C C R$	$b p B C C$	$b p s$	$b ? p C M$	$b ? p C S G$	$b p g a m e$
1	179.45	125.26	143.89	125.26	87.71	136.08	107.38
2	173.26	163.22	173.26	163.22	114.19	176.21	142.64
3	337.64	327.79	328.59	327.79	328.57	319.10	319.44
4	277.11	256.76	277.11	256.76	129.38	128.83	176.35
5	341.14	312.71	312.72	312.71	308.86	308.87	300.48
6	228.34	178.08	178.82	178.08	174.04	174.05	175.05
7	719.58	719.58	719.58	805.58	715.86	715.94	711.45
8	275.71	256.08	275.71	256.08	275.96	277.01	252.08
9	163.59	119.15	163.59	119.15	74.97	74.24	105.56
10	360.94	360.94	360.94	453.85	378.34	366.72	425.69
11	327.79	327.79	327.79	341.00	330.65	332.22	323.86
12	1068.76	1068.76	1068.76	1785.27	904.61	1196.68	1107.24
13	338.97	266.29	338.97	266.29	191.13	343.04	231.35
14	796.45	747.88	751.77	747.88	629.80	751.77	642.50
15	511.49	511.49	511.49	558.07	516.04	511.49	509.90
16	416.70	330.00	330.60	330.00	326.95	330.60	325.23
17	329.94	329.94	329.94	331.50	292.67	329.94	305.89
18	266.57	248.43	258.16	248.43	220.14	258.16	234.00
19	180.37	157.07	159.78	157.07	137.05	159.78	142.24
20	124.24	124.24	124.24	176.57	128.81	148.19	158.80
21	105.24	78.07	105.24	78.07	52.42	105.24	72.46
22	208.34	159.03	161.62	159.03	146.79	161.62	150.46
23	217.04	187.74	194.74	187.74	185.27	194.74	175.19
24	204.11	190.10	204.11	190.10	150.29	206.12	178.13
25	508.15	435.29	444.33	435.29	442.78	444.33	426.13
26	8660.92	7981.69	8245.74	8990.80	7243.28	8150.97	7699.51

References 37

1	Leibenstein H. Allocative efficiency vs.“X-efficiency”［J］. The American Economic Review， 1966， 56（3）： 392-415.
2	Averch H， Johnson L L. Behavior of the firm under regulatory constraint［J］. The American Economic Review， 1962， 52（5）： 1052-1069.
3	李峰，王月，梁樑，等.具有共享产出固定和约束的DEA两阶段效率评价方法研究［J］.中国管理科学，2023， 31（11）： 268-278.
	Li Feng， Wang Yue， Liang Liang， et al. A two-stage data envelopment analysis approach for evaluating decision-making units with fixed-sum shared outputs［J］. Chinese Journal of Management Science，2023， 31（11）： 268-278.
4	何心巨，吴华清.开源还是节流？——我国商业银行效率、行为模式与所有制差异［J］.计量经济学报，2021，1（2）：318-345.
	He Xinju， Wu Huaqing. Scrimp or save？ Profit efficiency， heterogenous behavior and ownership in Chinese commercial banks［J］. China Journal of Econometrics，2021，1（2）：318-345.
5	刘传斌，代伟，余乐安，等.基于GCA-DEA-MSVC方法的高校科研平台评价预测研究［J］.中国管理科学，2022，30（3）：240-247.
	Liu Chuanbin， Dai Wei， Yu Lean， et al. Study on evaluation and prediction of scientific research platforms of universities using a GCA-DEA-MSVC methodology［J］. Chinese Journal of Management Science，2022，30（3）：240-247.
6	雷西洋，丁彦，李姚矿，等.一种考虑子公司竞合关系的跨国公司固定成本分摊方法［J］.系统工程理论与实践，2019， 39（7）： 1714-1720.
	Lei Xiyang， Ding Yan， Li Yaokuang， et al. A study on multinational corporations’ fixed cost allocation method with considering subsidiaries’ competition and cooperation relationship［J］.Systems Engineering-Theory and Practice，2019， 39（7）： 1714-1720.
7	戴前智，黄西蒙，周思怡，等.考虑DEA要素相关性的我国区域工业水-能-环境效率评价研究［J］.系统科学与数学，2021，41（8）：2234-2251.
	Dai Qianzhi， Huang Ximeng， Zhou Siyi， et al. Measuring the water-energy-environmental DEA efficiency of China’s regional industries considering the factor correlation［J］.Journal of Systems Science and Mathematical Sciences，2021，41（8）：2234-2251.
8	朱庆缘，董学平，张珂铜，等.可再生能源电力配额指标动态分配机制研究［J］.系统工程理论与实践，2022，42（4）：967-980.
	Zhu Qingyuan， Dong Xueping， Zhang Ketong， et al. Research on dynamic allocation mechanism of renewables quota in renewable portfolio standard［J］.Systems Engineering- Theory and Practice， 2022， 42（4）： 967-980.
9	Li Jia， Wang Ping， Tao Xiangyang， et al. Productivity analysis for banks’ merger and acquisition using two-stage DEA： evidence from China［J］. Journal of Systems Science and Information， 2022， 9（6）： 627-659.
10	Ma Hewen， Geng Baoxia， Fu Yingxiong， et al. Efficiency analysis of industrial water treatment in China based on two-stage undesirable fixed-sum output DEA model［J］. Journal of Systems Science and Information， 2022， 9（6）： 660-680.
11	Bogetoft P. DEA-based yardstick competition： The optimality of best practice regulation［J］. Annals of Operations Research， 1997， 73： 277-298.
12	Varmaz A， Varwig A， Poddig T. Centralized resource planning and yardstick competition［J］. Omega， 2013， 41（1）： 112-118.
13	Lozano S， Villa G. Centralized resource allocation using data envelopment analysis［J］. Journal of Productivity Analysis， 2004， 22（1）： 143-161.
14	Afsharian M， Ahn H， Thanassoulis E. A DEA-based incentives system for centrally managed multi-unit organisations［J］. European Journal of Operational Research， 2017， 259（2）： 587-598.
15	Davtalab-Olyaie M， Mahmudi-Baram H， Asgharian M. Incentivizing units in centralized systems： a slacks-based approach［J］. Journal of the Operational Research Society， 2022， 73（8）： 1724-1741.
16	Afsharian M， Ahn H， Thanassoulis E. A frontier-based system of incentives for units in organisations with varying degrees of decentralisation［J］. European Journal of Operational Research， 2019， 275（1）： 224-237.
17	Afsharian M. A metafrontier-based yardstick competition mechanism for incentivising units in centrally managed multi-group organisations［J］. Annals of Operations Research， 2020， 288： 681-700.
18	Dai Qianzhi， Li Yongjun， Lei Xiyang， et al. A DEA-based incentive approach for allocating common revenues or fixed costs［J］. European Journal of Operational Research， 2021， 292（2）： 675-686.
19	An Qingxian， Tao Xiangyang， Xiong Beibei， et al. Frontier-based incentive mechanisms for allocating common revenues or fixed costs［J］. European Journal of Operational Research， 2022， 302（1）： 294-308.
20	Liang Liang， Wu Jie， Cook W D， et al. The DEA game cross-efficiency model and its Nash equilibrium［J］. Operations Research， 2008， 56（5）： 1278-1288.
21	Wu Jie， Liang Liang， Yang Feng， et al. Bargaining game model in the evaluation of decision making units［J］. Expert Systems with Applications， 2009， 36（3）： 4357-4362.
22	Zha Yong， Liang Liang. Two-stage cooperation model with input freely distributed among the stages［J］. European Journal of Operational Research， 2010， 205（2）： 332-338.
23	An Qingxian， Yang Min， Chu Junfei， et al. Efficiency evaluation of an interactive system by data envelopment analysis approach［J］. Computers & Industrial Engineering， 2017， 103： 17-25.
24	杨敏，费锡玥，魏宇琪，等.基于资源共享与子系统交互的两阶段DEA评价方法——兼对我国“一流大学”科研绩效的评价［J］.中国管理科学， 2022， 30（2）： 256-263.
	Yang Min， Fei Xiyue， Wei Yuqi， et al. Two-stage DEA evaluation method based on resource sharing and subsystem interaction： evaluation of scientific research performance for “first-class” universities in China［J］.Chinese Journal of Management Science， 2022， 30（2）： 256-263.
25	安庆贤，陈晓红，余亚飞，等.基于DEA的两阶段系统中间产品公平设定研究［J］.管理科学学报，2017，20（1）：32-40.
	An Qingxian， Chen Xiaohong， Yu Yafei， et al. Fair setting for intermediate products in two-stage system based on DEA［J］. Journal of Management Sciences in China，2017，20（1）：32-40.
26	Jahangoshai Rezaee M， Shokry M. Game theory versus multi-objective model for evaluating multi-level structure by using data envelopment analysis［J］. International Journal of Management Science and Engineering Management， 2017， 12（4）： 245-255.
27	刘文丽，王应明，吕书龙.基于交叉效率和合作博弈的决策单元排序方法［J］.中国管理科学，2018，26（4）：163-170.
	Liu Wenli， Wang Yingming， Lv Shulong. Ranking decision making units based on cross-efficiency and cooperative game［J］.Chinese Journal of Management Science，2018，26（4）：163-170.
28	Li Yongjun， Xie Jianhui， Wang Meiqiang， et al. Super efficiency evaluation using a common platform on a cooperative game［J］. European Journal of Operational Research， 2016， 255（3）： 884-892.
29	Andersen P， Petersen N C. A procedure for ranking efficient units in data envelopment analysis［J］. Management Science， 1993， 39（10）： 1261-1264.
30	张各兴，夏大慰.中国输配电网技术效率与全要素生产率研究——基于2005-2009年24家省级电力公司面板数据的分析［J］.财经研究，2012，38（10）：112-122.
	Zhang Gexing， Xia Dawei. Study on technical efficiency and total factor productivity of transmission and distribution grid in China： analysis based on panel data of 24 provincial power companies from 2005 to 2009［J］.Journal of Finance and Economics，2012，38（10）：112-122.
31	Li Hongzhou， Kopsakangas-Savolainen M， Xiao Xingzhi， et al. Cost efficiency of electric grid utilities in China： a comparison of estimates from SFA-MLE， SFA-Bayes and StoNED-CNLS［J］. Energy Economics， 2016， 55： 272-283.
32	李宏舟，李秀凤，赵宇婷，等.我国电网企业可节约成本的测算——基于标尺竞争规制的探索性研究［J］.产业组织评论，2019，13（3）：36-66.
	Li Hongzhou， Li Xiufeng， Zhao Yuting， et al. An estimation of cost-saving by electric grid sector of China： an exploratory study based on yardstick regulation［J］.Industrial Organization Review，2019，13（3）：36-66.
33	Bogetoft P. Performance benchmarking： measuring and managing performance［M］. New Haven， Springer Science & Business Media， 2013.
34	Glicksberg I L. A further generalization of the Kakutani fixed point theorem， with application to Nash equilibrium points［J］. Proceedings of the American Mathematical Society， 1952， 3（1）： 170-174.
35	Debreu G. A social equilibrium existence theorem［J］. Proceedings of the National Academy of Sciences， 1952， 38（10）： 886-893.
36	Brouwer L E J. Über abbildung von mannigfaltigkeiten［J］. Mathematische Annalen， 1911， 71（1）： 97-115.
37	Becker R A， Chakrabarti S K. Satisficing behavior， Brouwer’s fixed point theorem and Nash equilibrium［J］. Economic Theory， 2005， 26（1）： 63-83.

DMU	2016	2017	2018	2019	均值	方差
1	0.7987	0.7821	0.5857	0.5984	0.6912	0.0099
2	0.8237	0.8040	0.8274	0.8233	0.8196	0.0001
3	0.9209	0.8957	0.9414	0.9461	0.9260	0.0004
4	0.9712	0.9133	0.9410	0.6364	0.8655	0.0179
5	0.8700	0.8662	0.8496	0.8808	0.8666	0.0001
6	0.7516	0.7211	0.7118	0.7666	0.7378	0.0005
7	0.9326	1.0045	0.9656	0.9887	0.9729	0.0007
8	0.9522	0.9285	0.9381	0.9143	0.9333	0.0002
9	0.6417	0.6661	0.6866	0.6453	0.6599	0.0003
10	1.2105	1.2429	1.1879	1.1794	1.2052	0.0006
11	0.9607	0.8995	0.9827	0.9880	0.9577	0.0012
12	1.1702	1.0924	1.0794	1.0360	1.0945	0.0023
13	0.7053	0.7132	0.6637	0.6825	0.6912	0.0004
14	0.8657	0.8791	0.8730	0.8067	0.8561	0.0008
15	1.3423	1.1377	1.2510	0.9969	1.1820	0.0167
16	0.8887	0.8984	0.9154	0.7805	0.8707	0.0028
17	0.6612	0.6274	0.6773	0.9271	0.7232	0.0142
18	0.8369	0.8482	0.8614	0.8778	0.8561	0.0002
19	0.5965	0.6937	0.6560	0.7886	0.6837	0.0049
20	1.1473	1.2355	1.2041	1.2782	1.2163	0.0023
21	0.6395	0.6482	0.7046	0.6885	0.6702	0.0007
22	0.6266	0.6497	0.6236	0.7222	0.6555	0.0016
23	0.6220	0.6754	0.6760	0.8072	0.6951	0.0047
24	0.8049	0.7711	0.8792	0.8727	0.8320	0.0021
25	0.8836	0.8724	0.8155	0.8386	0.8526	0.0007

[1]	Hongwei Zhu,Lijun Tian,Xiaolan Jiang. Differentiated Incentive-based Management Strategies to Encourage Green Travel Behaviors in a Multi-mode Travel Scenario [J]. Chinese Journal of Management Science, 2024, 32(9): 131-141.
[2]	Yanfen Zhang,Qi Xu,Zhongmiao Sun. Dynamics of Contract Design for Platform Supply Chain with Competing Suppliers under Moral Hazard [J]. Chinese Journal of Management Science, 2024, 32(9): 160-170.
[3]	Xiaoxue Zhang,Jicai Liu. Research on the Risk Management Incentive Effect of Financial Institutions' Early Intervention in PPP Projects [J]. Chinese Journal of Management Science, 2024, 32(7): 54-64.
[4]	Zhengchi Liu,Bo Liang,Tao Ma. Reward Size, Ability Distribution and Incentive Effects of Crowdsourcing: A Model Analysis on All-Pay Auctions [J]. Chinese Journal of Management Science, 2024, 32(6): 13-21.
[5]	Zhongmiao Sun,Qi Xu,Yanfen Zhang. Dynamic Incentive Contract of On-Demand Service Platform with Different Types of Agents under Asymmetric Information [J]. Chinese Journal of Management Science, 2024, 32(5): 241-253.
[6]	Guangyu Wan,Feiyan Pu,Zichun Li,Yu Cao. Impact of Marketing Capability and Production Operation Capability on Firms' Financial Performance [J]. Chinese Journal of Management Science, 2024, 32(5): 275-285.
[7]	Heng Chen,Cheng Peng,Shuang Guo,Zhi Yang,kai Qi. Two-stage Evolution Analysis of Green Technology Innovation Diffusion Based on Complex Market Network [J]. Chinese Journal of Management Science, 2024, 32(3): 135-144.
[8]	Kai Zhao,Lei Li. Study on the Influence of Government Multi-tool Combination on Enterprise Innovation Behavior [J]. Chinese Journal of Management Science, 2024, 32(2): 221-230.
[9]	Weiwei Li,Pingtao Yi,Lu Wang. Situation Oriented Evaluation Approaches Based on Behavior Characteristics Analysis and the Application [J]. Chinese Journal of Management Science, 2024, 32(10): 171-180.
[10]	Yan-hui HOU,Min GUAN,Jia-kun WANG,Fan MENG,Hao ZHANG. Research on the Incentive Mechanism of Network Public Opinion Guidance Based on Differential Game in the Omnimedia Era [J]. Chinese Journal of Management Science, 2023, 31(8): 239-252.
[11]	Jian-bo CUI,Zheng-ying LUO. Cost Control and Ratchet Effect: Sharing Saving Incentive Mechanism vs. Target Incentive Mechanism [J]. Chinese Journal of Management Science, 2023, 31(8): 90-99.
[12]	NIU Yu-fei, ZHANG Fa-ming, YUAN Sheng-jun. Dynamic Evaluation with Generic Reinforcement Incentives and Its Application [J]. Chinese Journal of Management Science, 2023, 31(6): 241-252.
[13]	ZHOU Zhen, JIAN Hong-yu, HUANG Jia-pei, LIN Yun. The Influence of E-marketing on Cinema Performance Based on DEA and Grey Entropy [J]. Chinese Journal of Management Science, 2023, 31(5): 240-248.
[14]	LINGHU Da-zhi, WU Xin-li, LI Yi-na, YEI Fei. Impact Mechanism of Low-carbon Classification Standards on Carbon Emission Decisions of Heterogeneous Corporate [J]. Chinese Journal of Management Science, 2023, 31(4): 46-55.
[15]	JI Qing-kai, ZHANG Feng-lin, FANG Gang, HU Xiang-pei. Game Model of Blockchain Adoption and Product Pricing in Retail Supply Chain [J]. Chinese Journal of Management Science, 2023, 31(3): 102-112.

Cost Compensation Method for Incentives Based on Dynamic Non-cooperative Game and Super-efficiency DEA

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 5

References 37

Related Articles 15

Metrics

Comments

Recommended 0