We study a non-preemptive strictly periodic scheduling problem. This problem arises for example in the avionic field where a set of N periodic tasks (measure of a sensor, data presentation, etc.) has to be scheduled on P processors distributed on the plane. In this article, we consider an existing heuristic which is based on the notion of equilibrium. Following a game theory analogy, each task tries successively to optimize its own schedule and therefore to produce the best response, given the other schedules. We present a new method to compute the best response, and a propagation mechanism for non-overlapping constraints, which signi cantly improves this heuristic. These improvements allow the heuristic to compare favorably with MILP solutions.