Job-scheduling games have traditionally assumed fixed processing times. However, in many realistic environments, ranging from cyber-security response to high-frequency trading, a task's duration depends on its starting time. We study job-scheduling games with time-dependent processing times, where job lengths are linear functions of their start times, exhibiting either positive deterioration (increasing length) or negative deterioration (decreasing length). We analyze these games under various coordination mechanisms and priority policies. By introducing the concept of delay-averse agents, we provide a unifying framework to characterize equilibrium existence. For delay-averse jobs, we show that stability is maintained and pure Nash equilibria (NE) can be computed efficiently. In contrast, for non-delay-averse jobs, we demonstrate that a NE may not exist, and prove that deciding its existence is NP-complete, even on identical machines - a fundamental departure from classical coordination mechanisms. Regarding equilibrium inefficiency, we show that the Price of Anarchy (PoA) can be significantly higher than in environments with fixed processing times. To mitigate this, we propose and analyze three coordination mechanisms: SBPT (Shortest Basic Processing Time), which reduces the PoA in games with positive deterioration to a constant, and SDR (Smallest Deterioration Rate) and LBDR (Largest Basic-Deterioration Ratio) for negative deterioration, which achieve tight constant PoA bounds of $2$ and $\max\{\frac{e}{e-1}, 2-\frac{1}{m}\}$, respectively. Our results bridge the gap between centralized time-dependent scheduling and decentralized game-theoretic analysis.

翻译：传统作业调度博弈通常假设处理时间为固定值。然而，在从网络安全响应到高频交易等多种现实场景中，任务时长取决于其开始时间。本文研究具有时间依赖处理时间的作业调度博弈，其中作业长度为其开始时间的线性函数，呈现正劣化（长度增加）或负劣化（长度减少）。我们在多种协调机制和优先级策略下分析这类博弈。通过引入延迟厌恶型智能体概念，我们提供了统一的框架来刻画均衡存在性。对于延迟厌恶型作业，我们证明稳定性得以维持且纯纳什均衡可高效计算；而对于非延迟厌恶型作业，我们证明纳什均衡可能不存在，且验证其存在性的判定问题即使在同构机器上也是NP完全的，这与经典协调机制存在根本性差异。在均衡无效率方面，我们发现无政府状态价格可能显著高于固定处理时间场景。为缓解这一问题，我们提出并分析了三种协调机制：最短基本处理时间机制可将正劣化博弈的无政府状态价格降低为常数；针对负劣化场景，最小劣化率与最大基本-劣化比机制分别实现了紧的常数无政府状态价格界$2$和$\max\{\frac{e}{e-1}, 2-\frac{1}{m}\}$。我们的研究弥合了集中式时间依赖调度与分散式博弈分析之间的鸿沟。