Trade with enemy: Economic interdependence and stability under anarchy

This paper considers the problem of allocating resources between economic goods and military goods in a contest model. We characterize the equilibrium and its stability in both cases where the two states' economic goods are substitutes and complements, and compare the outcomes. If the two states' economic goods are substitutes, there may exist multiple equilibria including at least one unstable equilibrium when a state has a comparative advantage in a sector. Without any such comparative advantage, a unique stable equilibrium results in which both states build-up the same level of military goods regardless of their relative sizes. A unique stable equilibrium also emerges if the two states' economic goods are complements with Cobb–Douglas utility characteristics. These results suggest that greater economic interdependence due to the complementarity slows down the arms races, and help stabilize the system. If the contest between the two states is a winner-take-all all-pay auction, there exists a pure strategy equilibrium. In this equilibrium, the state with an absolute advantage in the military sector takes all the resources by spending slightly more in the military sector than the other state. Such a finding contradicts most of the standard all-pay auctions, in which only a mixed strategy equilibrium exists.