When does the private provision of a public good prevent conflict?

We consider a two-stage model, in which n players with the same preferences and different incomes compete for a common value prize and then contribute to a pure public good. We derive the sufficient and necessary condition under which there exists a Subgame Perfect Equilibrium in which a contest is not held. In particular, in order to maintain peace, the “poorest” player needs to contribute to the public good in every realization and therefore cannot be too poor. Peace therefore depends on the strength of the weakest player as well as on the value of the prize. The model may help in understanding conflicts between countries with a common interest.