个人简介

单而芳，伟德永久官网教授，博士生导师，上海市浦江人才。北京理工大学硕士、伟德永久官网运筹学与控制论专业博士，香港理工大学工商伟德永久官网博士后。曾先后在韩国国立昌原大学、韩国岭南大学、香港理工大学、澳大利亚墨尔本大学、香港科技大学和荷兰蒂尔堡大学做访问学者。

现主持国家自然科学基金面上项目1项，参与其他国家自然科学基金面上项目2项。已连续主持国家自然科学基金面上项目4项，并作为主要成员参加国家自然科学基金重点项目1项，其他国家自然科学基金5项。在J. Graph Theory、SIAM Discrte Math.、European J. Combin、Discrete Math等期刊上发表论文150余篇。近年来，开展了图上合作博弈与决策及相关经济管理问题的研究，相关研究成果发表在Int J Game Theory、Annals of Operations Research、Operations Research Letters、Mathematical Social Sciences、《系统工程理论与实践》和《中国管理科学》等知名期刊上。科研成果曾获上海市自然科学奖。

欢迎来自不同背景的同学报考研究生，有经济/数学/图论或计算机等理工背景的同学报考博士研究生。

教育背景：

博士，运筹学与控制论，伟德永久官网；

硕士，应用数学，北京理工大学；

学士，数学，河北师范大学。

工作经历：

2012.03 - 至今：伟德永久官网，教授；

2008.03-2012.03：伟德永久官网理学院，教授；

2001.03-2008.03：伟德永久官网理学院，副教授。

学术任职：

中国运筹学会图论与组合分会常务理事；

中国运筹学会博弈论分会常务理事；

中国工业与应用数学学会图论组合及应用专业委员会理事；

上海市运筹学会常务理事

美国数学会《Mathematical Reviews》特邀评论员；

欧洲数学会《Zentralblatt MATH》特邀评论员。

主讲课程：

本科：《运筹学》

博士：《博弈论》、《运筹学》、《建模、优化、评价理论与方法》

MBA：《数据、模型与决策》

代表性论文 (合作博弈与决策)：

1. Erfang Shan, Marginality and a characterization of the Owen graph value. International Journal of Game Theory, https://doi.org/10.1007/s00182 -022- 00825-0.

2. Liying Kang, Anna Khmelnitskaya, Erfang Shan, Dolf Talman, Guang Zhang. The two-step average tree value for graph and hypergraph games. Annals of Operations Research, https://doi.org/10.1007/s10479-022-04966-z.

3. Erfang Shan, Zhiqiang Yu, Wenrong Lyu, Union-wise egalitarian solutions in cooperative games with a coalition structure. 4OR, https://doi.org/10.1007/ s10288-022-00529-x.

4. Erfang Shan, Jilei Shi, Wenrong Lyu. The efficient partition surplus Owen graph value. Annals of Operations Research, 2023, 320:379-392.

5. Daniel Li Li, Erfang Shan, Tree solutions and standardness for cycle-free graph games. Economics Letters , 2023, 222: 110955.

6. Daniel Li Li, Erfang Shan. Safety of links with respect to the Myerson value for communication situations. Operational Research, 2022, 22: 2121-2131.

7. Erfang Shan, Wenrong Lyu, Jilei Shi, Shanshan Nie, Consistency and the graph Banzhaf value for communication graph games. Operations Research Letters, 2022, 50: 190-194.

8. Jilei Shi, Lei Cai, Erfang Shan, Wenrong Lyu. A value for cooperative games with coalition and probabilistic graph structures. Journal of Combinatorial Optimization, 2022, 43:646-671.

9. Daniel Li Li, Erfang Shan. Egalitarian allocation and players of certain type. Operations Research Letters, 2021, 49:492-495.

10. Jilei Shi, Erfang Shan. The Banzhaf value for generalized probabilistic communication situations. Annals of Operations Research, 2021, 301: 225–244.

11. Daniel Li Li, Erfang Shan. Cooperative games with partial information. International Journal of Game Theory, 2021, 50: 297-309.

12. Liying Kang, Anna Khmelnitskaya, Erfang Shan, Dolf Talman, Guang Zhang. The average tree value for hypergraph games. Mathematical Methods of Operations Research, 2021, 94: 437-460.

13. Jilei Shi, Erfang Shan. Weighted component-wise solutions for graph games. Economics Letters, 2020, 192: 109-233.

14. Daniel Li Li, Erfang Shan. Efficient quotient extensions of the Myerson value. Annals of Operations Research, 2020, 292: 171–181.

15. Daniel Li Li, Erfang Shan. The Myerson value for directed graph games. Operations Research Letters, 2020, 48: 42-46.

16. Daniel Li Li, Erfang Shan. Marginal contributions and derivatives for set functions in cooperative games. Journal of Combinatorial Optimization, 2020, 39: 849–858.

17. Daniel Li Li, Erfang Shan, Marginal contributions and derivatives for set functions in cooperative games, Journal of Combinatorial Optimization, 2020, 39: 849–858.

18. Erfang Shan, Jilei Shi, Wenrong Lv, A Note on the Position Value for Hypergraph Communication Situations, in D.-Z. Du and J. Wang (Eds.): Ko Festschrift, Lecture Notes in Computer Science 12000, pp. 230-237, 2020.

19. Erfang Shan, Jiayu Han, Jilei Shi. The efficient proportional Myerson values. Operations Research Letters, 2019, 47: 574-578.

20. Daniel Li Li, Erfang Shan. The Myerson value on local structures of coalitions. Journal of the Operations Research Society of China, 2019, 7: 461-473.

21. Erfang Shan, Guang Zhang. The degree value for games with communication structure. International Journal of Game Theory, 2018, 47: 857-871.

22. Daniel Li Li, Erfang Shan, Cost sharing on prices for games on graphs, Journal of Combinatorial Optimization, 2017, 34:676–688.

23. Guang Zhang, Erfang Shan, Liying Kang, Yanxia Dong, Two efficient values of cooperative games with graph structure based on τ-values. Journal of Combinatorial Optimization, 2017, 34: 462-482.

24. Erfang Shan, Guang Zhang, Yanxia Dong, Component-wise proportional solutions for communication graph games. Mathematical Social Sciences, 2016, 81: 22-28.

25. 单而芳. 河流洪水风险控制的合作博弈分析. 中国管理科学. 10.16381/j.cnki. issn1003-207x.2021.0105

26. 单而芳, 史纪磊, 蔡蕾. 具有联盟和概率图结构合作对策的分配规则及其应用. 中国管理科学. 10.16381/j.cnki.issn1003-207x.2020.1348

27. 单而芳, 曾晗, 韩佳玉. 无圈超图对策上的有效平均树解. 系统工程理论与实践, 2021, 41(3): 781-789.

28. 单而芳, 史纪磊, 吕文蓉等. 具有图限制通信结构对策的有效 Owen 值. 中国科学: 数学, 2020, 50(9): 1219-1232.

29. 李理, 单而芳. 图上博弈的Page-Shapley值. 系统工程理论与实践, 2019, 39(11): 2771-2783.

30. 单而芳, 梁莉敏, 张广. 基于限制博弈的具有容量限制的易腐品联合运输费用分摊问题. 中国管理科学, 2018, 26(9): 97-105.