  The dynamics of ``vicious'', continuously growing civilizations (domains),
which engage in ``war'' whenever two domains meet, is investigated. In the war
event, the smaller domain is annihilated, while the larger domain is reduced in
size by a fraction $\e$ of the casualties of the loser. Here $\e$ quantifies
the fairness of the war, with $\e=1$ corresponding to a fair war with equal
casualties on both side, and $\e=0$ corresponding to a completely unfair war
where the winner suffers no casualties. In the heterogeneous version of the
model, evolution begins from a specified initial distribution of domains, while
in the homogeneous system, there is a continuous and spatially uniform input of
point domains, in addition to the growth and warfare. For the heterogeneous
case, the rate equations are derived and solved, and comparisons with numerical
simulations are made. An exact solution is also derived for the case of equal
size domains in one dimension. The heterogeneous system is found to coarsen,
with the typical cluster size growing linearly in time $t$ and the number
density of domains decreases as $1/t$. For the homogeneous system, two
different long-time behaviors arise as a function of $\e$. When $1/2<\e\leq 1$
(relatively fair wars), a steady state arises which is characterized by
egalitarian competition between domains of comparable size. In the limiting
case of $\e=1$, rate equations which simultaneously account for the
distribution of domains and that of the intervening gaps are derived and
solved. The steady state is characterized by domains whose age is typically
much larger than their size. When $0\leq\e<1/2$ (unfair wars), a few
``superpowers'' ultimately dominate. Simulations indicate that this coarsening
process is characterized by power-law temporal behavior, with non-universal
