Defense and Welfare Under Rivalry

Two small countries facing a constant probability of war with each other import arms for consumption goods from the rest of the world. The defense good, produced by combining arms and army, is a public good. The reaction curve depicting the optimal supply of the defense good turns out to be backward-bending. Nevertheless, at least one of the reaction curves is positively sloped at the unique Nash equilibrium. Several comparative statics results are derived. For example, if one country's reaction curve is negatively sloped, military aid to the rival leads to a decline in its optimal supply of the defense good