We consider a game-theoretic variant of an interval scheduling problem. Every job is associated with a length, a weight, and a color. Each player controls all the jobs of a specific color, and needs to decide on a processing interval for each of its jobs. Jobs of the same color can be processed simultaneously by the machine. A job is covered if the machine is configured to its color during its whole processing interval. The goal of the machine is to maximize the sum of weights of all covered jobs, and the goal of each player is to place its jobs such that the sum of weights of covered jobs from its color is maximized. The study of this game is motivated by several applications like antenna scheduling for wireless networks. We first show that given a strategy profile of the players, the machine scheduling problem can be solved in polynomial time. We then study the game from the players' point of view. We analyze the existence of Nash equilibria, its computation, and inefficiency. We distinguish between instances of the classical interval scheduling problem, in which every player controls a single job, and instances in which color sets may include multiple jobs.

翻译：本文研究区间调度问题的一个博弈论变体。每个任务关联一个长度、一个权重和一种颜色。每个参与者控制特定颜色的所有任务，并需要为其每个任务决定一个处理区间。同一颜色的任务可由机器同时处理。若机器在其整个处理区间内配置为该任务的颜色，则该任务被覆盖。机器的目标是最大化所有被覆盖任务的权重之和，而每个参与者的目标是放置其任务，使得其颜色中被覆盖任务的权重之和最大化。研究该博弈的动机源于无线网络天线调度等多个应用。我们首先证明，给定参与者的策略组合，机器调度问题可在多项式时间内求解。随后从参与者视角研究该博弈，分析纳什均衡的存在性、计算方法及其效率损失。我们区分了经典区间调度问题实例（每个参与者控制单个任务）与颜色集合可能包含多个任务的实例。