  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
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 non-linear deviation penalties.

Computer Science and Game Theory