文章研究~$m$ 台平行机排序博弈问题的混合协调机制. 混合协调机制允许机 器各自选择遵从不同的规则. 主要研究工件费用定义为工件自身完工时间的同型机排序问题在混合协调机制下的纳什均衡, 给出了能够得到纳什均衡的算法. 对于有服务等级的排序博弈问题, 考虑了两类低等级优先~(LG) 和高等级优先~(HG) 规则混合的协调机制. 第一类混合协调机制中机器各自选择遵从LG 规则或~HG 规则. 第二类混合协调机制要求前~$h$ 台机器遵从同一种规则, 后~$m-h$ 台机器遵从另一种规则. 通过衡量无政府代价~(Price of Anarchy), 估计了在系统目标为极小化工件最大完工时间时, 机器遵从的规则和工件对机器的自主选择对整个系统效益的影响.

In this paper, we study scheduling games under hybrid coordination mechanisms in which $m$ parallel machines are allowed to follow different policies. We present an algorithm to show that Nash equilibriums always exist. For scheduling games with grade of service (GoS), we consider two kinds of hybrid coordination mechanisms with LG (Lowest Grade first) policy and HG (Highest Grade first) policy. The first one enables every machine to choose either LG policy or HG policy independently. The second hybrid coordination mechanism requires the first $h$ machines follow one policy and the last $m-h$ machines follow the other. Inefficiency of Nash equilibria is also evaluated when the social cost is minimizing the makespan by estimating the Price of Anarchy.