  This short note studies the simple arithmetic properties of multi-year bonus
allocation systems, as recently implemented in the population of
teacher-researchers, with the PEDR on the one hand, and with component 3 of the
RIPEC on the other.In the first stage, we study an initial model in which the
entire population applies, in order to highlight the effect of the multi-year
nature of the award: the success rate of an application is very different from
the frequency with which an individual receives the bonus.Secondly, we take
into account the fact that part of the population is not a candidate, with
cross-influences between the competition participation rate and the individual
success rate.In the light of available statistics on agent behavior, we will
discuss the possibility of RIPEC training a large part of the population.
