The purpose of this paper is to obtain insight into conditions under which a resource exchange alliance can provide greater profit than the setting without an alliance, and to propose a model to design a resource exchange alliance. We first consider a setting in which customers want a combined product assembled from products sold by different sellers. We show that without an alliance the sellers will tend to price their products too high and sell too little, thereby foregoing potential profit, especially when capacity is large. This provides an economic motivation for interest in alliances, because the hope may be that some of the foregone profit may be captured under an alliance. We then consider a resource exchange alliance, including the effect of the alliance on competition among alliance members. We show that the foregone profit may indeed be captured under such an alliance. The problem of determining the optimal amounts of resources to exchange is formulated as a stochastic mathematical program with equilibrium constraints. We show how to determine whether there exists a unique equilibrium after resource exchange, how to compute the equilibrium, and how to compute the optimal resource exchange.