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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. Thejobs' sizes are homogeneous and deterministic. Each job belongs to a singledecision maker, a customer, who aims to arrive at a time that minimizes hisdeviation penalty. If multiple customers arrive at the same time then theirorder of service is determined by a uniform random draw. We show that if thecost function has a weighted absolute deviation form then any Nash equilibriumis pure and symmetric, that is, all customers arrive together. Furthermore, weshow that there exist multiple, in fact a continuum, of equilibrium arrivaltimes, and provide necessary and sufficient conditions for the socially optimalarrival time to be an equilibrium. The base model is solved explicitly, but theprevalence of a pure symmetric equilibrium is shown to be robust to severalrelaxations of the assumptions: restricted server availability, inclusion ofsmall waiting costs, stochastic job sizes, randomly sized population,heterogeneous due dates, and non-linear deviation penalties.

A strategic model of job arrivals to a single machine with earliness and tardiness penalties