Sequential scheduling on identical machines

We study a sequential version of the well-known KP-model: Each of n agents has a job that needs to be processed on any of m machines. Agents sequentially select a machine for processing their jobs. The goal of each agent is to minimize the finish time of his machine. We study the corresponding sequential price of anarchy for m identical machines under arbitrary and LPT orders, and suggest insights into the case of two unrelated machines.