Peace through bribing

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.