  We study a model in which before a conflict between two parties escalates
into a war (in the form of an all-pay auction), a party can offer a
take-it-or-leave-it bribe to the other for a peaceful settlement. In contrast
to the received literature, we find that peace security is impossible in our
model. We characterize the necessary and sufficient conditions for peace
implementability. Furthermore, we find that separating equilibria do not exist
and the number of (on-path) bribes in any non-peaceful equilibria is at most
two. We also consider a requesting model and characterize the necessary and
sufficient conditions for the existence of robust peaceful equilibria, all of
which are sustained by the identical (on-path) request. Contrary to the bribing
model, peace security is possible in the requesting model.
