We study the online version of the classical parallel machine

scheduling problem to minimize the total weighted completion time

from a new perspective: We assume that the data of each job,

namely its release date $r_j$, its processing time $p_j$ and its

weight $w_j$ is only known to the job itself, but not to the

system. Furthermore, we assume a decentralized setting where jobs

choose the machine on which they want to be processed themselves.

We study this problem from the perspective of algorithmic

mechanism design. We introduce the concept of a myopic best

response equilibrium, a concept weaker than the dominant strategy

equilibrium, but appropriate for online problems. We present a

polynomial time, online scheduling mechanism that, assuming

rational behavior of jobs, results in an equilibrium schedule that

is 3.281-competitive. The mechanism deploys an online payment

scheme that induces rational jobs to truthfully report their

private data. We also show that the underlying local scheduling

policy cannot be extended to a mechanism where truthful reports

constitute a dominant strategy equilibrium.