摘要
基于合作博弈理论,将单人On-line Ski问题扩展到了双人情形.研究了一个在线决策者和一个离线决策者的合作博弈模型,给出了具有最小竞争比的IRBIS策略,求出了双方合作分担成本的纳什均衡解,并进行了数值模拟.结论显示:两个滑雪者合作的优势出现在在线滑雪者滑雪终止时间较小的情形下;两个滑雪者合作的效率与滑雪时间的重合程度负相关,但滑雪重合程度一般不影响竞争比的下界(个别特殊情形除外);另外,滑雪重合程度增大的过程中,双方合作效率下降的速度逐渐减小.
Based on cooperative games, a model of two-people cooperated ski problem, which is an extension of the classical on-line ski problem for a single man, is studied. Our attention is first concentrated on the cooperation between on-line skiers and off-line skiers. We propose the IRBIS strategy which has the lower- bounding competitive ratio, and give the Nash equilibrium solution for the cooperation. A numerical study is conducted, and several conclusions are given： 1） The advantage of the cooperation happens in the condition that the on-line skier has a small ski terminal time. 2） The overlap ratio of ski time is significantly negatively correlated with the efficiency of the cooperation, but does not affect the lower-bounding competitive ratio except in one special case. 3） In the progression of the ski overlap ratio, the decreasing speed of the cooperation efficiency is slowing down.
出处
《系统工程学报》
CSCD
北大核心
2014年第4期468-476,共9页
Journal of Systems Engineering
基金
国家自然科学基金资助项目(71071113
71371141
71001080
71161016)
全国优秀博士论文作者专项资金资助项目(200782)
高等学校博士学科点专项科研基金资助项目(20100072110011)
关键词
在线租赁问题
竞争比
双人合作博弈
on-line renting-buying problem
competitive ratio
two-people cooperative game
