I am a job. In job-scheduling applications, my friends and I are assigned to machines that can process us. In the last decade, thanks to our strong labor union, and the rise of algorithmic game theory, we are getting more and more freedom regarding our assignment. Each of us acts to minimize his own cost, rather than to optimize a global objective.

My goal is different. I am a secret agent operated by the system. I do my best to lead my fellow jobs to an outcome with a high social cost. My naive friends keep doing the best they can, each of them performs his best-response move whenever he gets the opportunity to do so. Luckily, I am a charismatic guy. I can determine the order according to which the naive jobs perform their best-response moves. In this paper, I analyze my power, formalized as the Price of a Traitor (PoT), in cost-sharing scheduling games – in which we need to cover the cost of the machines that process us.

Starting from an initial Nash Equilibrium (NE) profile, I join the instance and hurt its stability. A sequence of best-response moves is performed until I vanish, leaving the naive jobs in a new NE. For an initial NE assignment, $S_0$, the PoT measures the ratio between the social cost of a worst NE I can lead the jobs to, starting from $S_0$, and the social cost of $S_0$. The PoT of a game is the maximal such ratio among all game instances and initial NE assignments.

My analysis distinguishes between instances with unit- and arbitrary-cost machines, and instances with unit- and arbitrary-length jobs. I give exact bounds on the PoT for each setting, in general and in symmetric games. While it turns out that in most settings my power is really impressive, my task is computationally hard (and also hard to approximate).

我是工作 在安排工作的应用程序中，我和我的朋友被分配到可以处理我们的计算机上。在过去的十年中，由于我们强大的工会以及算法博弈论的兴起，我们在分配工作方面获得了越来越多的自由。我们每个人的行为都是为了最小化自己的成本，而不是为了实现全球目标。

我的目标是不同的。我是系统操作的秘密特工。我尽我所能带领同伴取得高社会成本的结果。我的天真的朋友会继续努力，只要有机会，他们每个人都会做出最反应最快的动作。幸运的是，我是一个有超凡魅力的家伙。我可以确定幼稚作业执行其最佳响应动作的顺序。在本文中，我分析了我在分摊成本计划游戏中的权力，将其形式化为“叛徒的价格（PoT）”，其中我们需要支付处理我们的机器的成本。

从最初的Nash平衡（NE）配置文件开始，我加入了实例并损害了它的稳定性。执行一系列响应速度最快的动作，直到我消失，将幼稚的工作留在新的NE中。对于初始网元分配，${\mathrm{小号}}_0$，PoT衡量的是我可以领导的最差NE的社会成本与 ${\mathrm{小号}}_0$，以及 ${\mathrm{小号}}_0$。游戏的PoT是所有游戏实例和初始NE分配之间的最大比例。

我的分析将单位成本和任意成本机器的实例与单位长度和任意长度作业的实例区分开。在一般游戏和对称游戏中，我会为每种设置给出PoT的确切界限。事实证明，在大多数情况下，我的能力确实令人印象深刻，但我的任务在计算上很困难（而且也很难估算）。