不确定偏好序下的双边匹配博弈

doi:10.15960/j.cnki.issn.1007-6093.2020.01.013

运筹学学报 ›› 2020, Vol. 24 ›› Issue (1): 155-162.doi: 10.15960/j.cnki.issn.1007-6093.2020.01.013

• • 上一篇

不确定偏好序下的双边匹配博弈

林杨^1,2, 王应明^2,*

1. 福建师范大学经济学院, 福州 350107;
2. 福州大学决策科学研究所, 福州 350107

收稿日期:2017-12-25 发布日期:2020-03-09
通讯作者: 王应明 E-mail:msymwang@hotmail.com
基金资助:
国家社会科学基金（No.19BGL092）

Two-sided game matching with uncertain preference ordinal

LIN Yang^1,2, WANG Yingming^2,*

1. School of Economics, Fujian Normal University, Fuzhou 350107, China;
2. Decision Science Institute, Fuzhou University, Fuzhou 350107, China

Received:2017-12-25 Published:2020-03-09

摘要/Abstract

摘要： 针对带有不确定偏好序的双边匹配问题，现有方法大都仅注重整体收益之和，忽略了参与人的个体收益以及在交互选择中的策略运用.基于最大满意度准则，给出不确定序下的收益（满意度）矩阵的推导过程；然后，从个体理性视角，结合矩阵博弈的思想构建一种兼顾整体和个体收益的博弈匹配优化模型，并证明模型最优解满足纳什均衡.最后，进一步探讨各种策略选择及其优劣分析.

关键词: 双边匹配, 不确定偏好序, 收益矩阵, 博弈匹配, 纳什均衡

Abstract: Owing to the problem of two-sided matching decision with uncertain preference ordinal (UPO), the existing methods mainly consider the overall payoff only. Yet the individual payoff and strategic operations during matching are often neglected in mutual choices. Based on the criteria of maximum satisfaction, a process for handling UPO is developed to derive payoff matrix. Then, a game-based matching model is built from the viewpoint of individual rational. This model takes account of both overall and individual payoff, which is combined with the idea of matrix game. Moreover, the results are proved to be Nash equilibrium. Finally, discussions on different strategic choices, as well as their advantages and limits analysis are presented.

Key words: two-sided matching, uncertain preference ordinal, payoff matrix, game matching, Nash equilibrium

中图分类号:

O221

林杨, 王应明. 不确定偏好序下的双边匹配博弈[J]. 运筹学学报, 2020, 24(1): 155-162.

LIN Yang, WANG Yingming. Two-sided game matching with uncertain preference ordinal[J]. Operations Research Transactions, 2020, 24(1): 155-162.

参考文献

[1] Roth A E. The economics of matching:Stability and incentives[J]. Mathematics of Operations Research, 1982, 7(4):617-628.
[2] 熊新生, 何琨, 赵勇. 弱偏好序下存在租客的房屋匹配问题机制设计[J]. 中国科学:信息科学, 2014, 44(9):1140-1155.
[3] Gale D, Shapley L S. College admissions and the stability of marriage[J]. The American Mathematical Monthly, 1962, 69(1):9-15.
[4] Carrabs F, Cerulli R, Gentili M. The labeled maximum matching problem[J]. Computers & Operations Research, 2009, 36(6):1859-1871.
[5] 樊治平, 李铭洋. 考虑稳定匹配条件的双边满意匹配决策方法[J]. 中国管理科学, 2009, 22(4), 113-118.
[6] Nash J. Non-cooperative games[J]. Annals of Mathematics, 1951, 54(2):286-295.
[7] Ha laburda H. Unravelling in two-sided matching markets and similarity of preferences[J]. Games and Economic Behavior, 2010, 69(2):365-393.
[8] Hurwicz L, Reiter S. Designing Economic Mechanisms[M]. Cambridge:Cambridge University Press, 2006.
[9] Corominas-Bosch M. Bargaining in a network of buyers and sellers[J]. Journal of Economic Theory, 2004, 115(1):35-77.
[10] Lin Y, Wang Y M, Chen S Q. Hesitant fuzzy multi-attribute matching decision making based on regret theory with uncertain weights[J]. International Journal of Fuzzy Systems, 2017, 19(4):955-966.
[11] Teo C P, Sethuraman J, Tan W P. Gale-Shapley stable marriage problem revisited:Strategic issues and applications[J]. Management Science, 2001, 47(9):1252-1267.
[12] Roth A E, Rothblum U G. Stable matchings, optimal assignments, and linear programming[J]. Mathematics of Operations Research, 1993, 18(4):803-828.
[13] Mindruta D, Moeen M, Agarwal R. A two-sided matching approach for partner selection and assessing complementarities in partners' attributes in inter-firm alliances[J]. Strategic Management Journal, 2016, 37(1):206-231.
[14] Wang X, Agatz N, Erera A. Stable matching for dynamic ride-sharing systems[J]. Transportation Science, 2017, 52(4):850-867.
[15] 樊治平, 乐琦. 基于完全偏好序信息的严格双边匹配方法[J]. 管理科学学报, 2014, 17(1):21-34.
[16] 乐琦, 樊治平. 基于不完全序值信息的双边匹配决策方法[J]. 管理科学学报, 2015, 18(2):23-35.
[17] 陈圣群. 基于分布式序关系的双边匹配决策方法[J]. 运筹与管理, 2016, 25(3):146-150.
[18] Fan Z P, Yue Q, Feng B. An approach to group decision-making with uncertain preference ordinals[J]. Computers & Industrial Engineering, 2010, 58(1):51-57.
[19] Huynh V N, Nakamori Y. A satisfactory-oriented approach to multi-expert decision-making with linguistic assessments[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 2005, 35(2):184-196.
[20] 李登峰. 模糊多目标多人决策与对策[M]. 北京:国防工业出版社. 2003.
[21] Ellison G. Cooperation in the Prisoner's Dilemma with anonymous random matching[J]. Review of Economic Studies, 1994, 61(3):567-588.
[22] 胡勋锋, 李登峰. 满意度优化运输问题[J]. 运筹学学报, 2014, 18(4):36-44.
[23] Shapley L S. A value for n-person games[J]. Annals of Mathematics Studies, 1953, 28:307-318.

不确定偏好序下的双边匹配博弈

Two-sided game matching with uncertain preference ordinal

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