  In the late sixties the Canadian psychologist Laurence J. Peter advanced an
apparently paradoxical principle, named since then after him, which can be
summarized as follows: {\it 'Every new member in a hierarchical organization
climbs the hierarchy until he/she reaches his/her level of maximum
incompetence'}. Despite its apparent unreasonableness, such a principle would
realistically act in any organization where the mechanism of promotion rewards
the best members and where the mechanism at their new level in the hierarchical
structure does not depend on the competence they had at the previous level,
usually because the tasks of the levels are very different to each other. Here
we show, by means of agent based simulations, that if the latter two features
actually hold in a given model of an organization with a hierarchical
structure, then not only is the Peter principle unavoidable, but also it yields
in turn a significant reduction of the global efficiency of the organization.
Within a game theory-like approach, we explore different promotion strategies
and we find, counterintuitively, that in order to avoid such an effect the best
ways for improving the efficiency of a given organization are either to promote
each time an agent at random or to promote randomly the best and the worst
members in terms of competence.
