A strategic model of job arrivals to a single machine with earliness and tardiness penalties
研究多个客户分散决策何时将作业提交给单台机器，每个客户都希望最小化偏离交期的惩罚，发现任何纳什均衡都是纯策略且对称的，即所有客户同时到达。
We consider a game of decentralized timing of jobs to a single server (machine) with a penalty for deviation from a due date, and no delay costs. The jobs’ sizes are homogeneous and deterministic. Each job belongs to a single decision maker, a customer, who aims to arrive at a time that minimizes his(her) deviation penalty. If multiple customers arrive at the same time, then their order of service is determined by a uniform random draw. We show that if the cost function has a weighted absolute deviation form, then any Nash equilibrium is pure and symmetric, that is, all customers arrive together. Furthermore, we show that there exist multiple, in fact a continuum, of equilibrium arrival times, and provide necessary and sufficient conditions for the socially optimal arrival time to be an equilibrium. The base model is solved explicitly, but the prevalence of a pure symmetric equilibrium is shown to be robust to several relaxations of the assumptions: restricted server availability, inclusion of small waiting costs, stochastic job sizes, randomly sized population, heterogeneous due dates, and nonlinear deviation penalties.