排序对策中的光滑不等式与均衡无效性
Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games
摘要：
我们研究调度游戏（与不相关的机器）的协调机制。在这些游戏中，每个任务代表一个玩家，玩家需要选择一台机器来执行任务，并打算尽可能早地完成任务。我们的目标是设计调度策略，总是承认一个纯粹的纳什均衡，并保证一个小的无政府代价的l_k-范数的社会成本-目标平衡整体服务质量和公平性。我们考虑的政策与不同数量的知识工作：非千里眼，强烈的本地和本地。分析依赖于光滑的论点连同适当的不等式，称为光滑不等式。在这个统一的框架下，我们能够证明以下结果。首先，我们研究了强地方性政策SPT和非透视性政策EQUI的l_k范数社会成本的无效率。证明了策略SPT的无政府无政府代价为O（k）。我们还证明了一个下界的欧米茄（k/log k）的所有确定性，非抢占式，强本地和非等待的政策（非等待政策产生的时间表没有空闲时间）。这些结果保证了SPT在l_k-范数社会成本类下接近最优。证明了非透视策略EQUI的无政府无政府代价为O（2^k）.其次，我们考虑的完工时间（l_infty-norm）的社会成本，通过连接的l_k-范数函数。我们重新审视一些地方的政策，并提供更简单，统一的证明框架的角度来看。在此基础上，提出了一种局部政策平衡的方法.该策略保证了O（log m）的无政府代价，这使得它成为当前最知名的匿名本地策略中的策略，总是允许一个纯纳什均衡。
英文摘要：
We study coordination mechanisms for Scheduling Games (with unrelated machines). In these games, each job represents a player, who needs to choose a machine for its execution, and intends to complete earliest possible. Our goal is to design scheduling policies that always admit a pure Nash equilibrium and guarantee a small price of anarchy for the l_k-norm social cost --- the objective balances overall quality of service and fairness. We consider policies with different amount of knowledge about jobs: non-clairvoyant, strongly-local and local. The analysis relies on the smooth argument together with adequate inequalities, called smooth inequalities. With this unified framework, we are able to prove the following results. First, we study the inefficiency in l_k-norm social costs of a strongly-local policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all deterministic, non-preemptive, strongly-local and non-waiting policies (non-waiting policies produce schedules without idle times). These results ensure that SPT is close to optimal with respect to the class of l_k-norm social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price of anarchy O(2^k). Second, we consider the makespan (l_infty-norm) social cost by making connection within the l_k-norm functions. We revisit some local policies and provide simpler, unified proofs from the framework's point of view. With the highlight of the approach, we derive a local policy Balance. This policy guarantees a price of anarchy of O(log m), which makes it the currently best known policy among the anonymous local policies that always admit a pure Nash equilibrium.
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