运筹学学报 >
2018 , Vol. 22 >Issue 1: 87 - 96
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2018.01.007
一类博弈排序问题的纳什均衡存在性证明
收稿日期: 2016-07-24
网络出版日期: 2018-03-15
基金资助
国家自然科学基金(Nos.11771251, 71771138), 山东省自然科学基金(Nos. ZR2015GZ009, ZR2017MG009), 曲阜师范大学博士科研创新资助基金
Existence of Nash equilibria in scheduling game on limited machines with activation cost
Received date: 2016-07-24
Online published: 2018-03-15
张龙, 张玉忠, 柏庆国 . 一类博弈排序问题的纳什均衡存在性证明 [J]. 运筹学学报, 2018 , 22(1) : 87 -96 . DOI: 10.15960/j.cnki.issn.1007-6093.2018.01.007
In this paper, we investigate game scheduling of jobs in two kinds of limited number of uniform machines with activation cost. The number of machines with speed 1 and activation cost B in the first category is limited. Similarly, the number of machines with speed a(>1) and activation cost aB in the second category is also limited. Jobs are served as self-interested players who choose a machine with the objective of minimizing their individual cost without considering other players' cost and the total social cost. A job's cost is composed of its machine's load and its share in the machine's activation cost, which is proportionally shared with respect to its size. We design different algorithms for different cases. Then, every assignment obtained by each different algorithm is proved to be a Nash equilibrium.
/
〈 |
|
〉 |