  Percolation plays an important role in fields and phenomena as diverse as the
study of social networks, the dynamics of epidemics, the robustness of
electricity grids, conduction in disordered media, and geometric properties in
statistical physics. We analyse a new percolation problem in which the first
order nature of an equilibrium percolation transition can be established
analytically and verified numerically. The rules for this site percolation
model are physical and very simple, requiring only the introduction of a weight
$W(n)=n+1$ for a cluster of size $n$. This establishes that a discontinuous
percolation transition can occur with qualitatively more local interactions
than in all currently considered examples of explosive percolation; and that,
unlike these, it can be reversible. This greatly extends both the applicability
of such percolation models in principle, and their reach in practice.
