  We consider a generalization of classic bootstrap percolation in which two
competing processes concurrently evolve on the same graph $G(n,p)$. Nodes can
be in one of three states, conveniently represented by different colors: red,
black and white. Initially, a given number $a_R$ of active red nodes (red
seeds) are selected uniformly at random among the $n$ nodes. Similarly, a given
number $a_B$ of active black nodes (black seeds) are selected uniformly at
random among the other $n-a_R$ nodes. All remaining nodes are initially white
(inactive). White nodes wake up at times dictated by independent Poisson clocks
of rate 1. When a white node wakes up, it checks the state of its neighbors: if
the number of red (black) neighbors exceeds the number of black (red) neighbors
by a fixed amount $r \geq 2$, the node becomes an active red (black) node, and
remains so forever. The parameters of the model are, besides $r$ (fixed) and
$n$ (tending to $\infty$), the numbers $a_R$ ($a_B$) of initial red (black)
seeds, and the edge existence probability $p=p(n)$. We study the size $A^*_R$
($A^*_B$) of the final set of active red (black) nodes, identifying different
regimes which are analyzed under suitable time-scales, allowing us to obtain
detailed (asymptotic) temporal dynamics of the two concurrent activation
processes.
