Nash’s demand game and resource-allocation

I consider Nash’s demand game (NDG) in the context of resource-allocation, rather than in the abstract utility space. If the resource is one-dimensional, the known results from the NDG literature are recovered: either the Nash solution is uniquely supported at the perturbations’ limit, or the entire (relative interior of the) Pareto frontier is supported; which case obtains depends on the type of perturbation. I show that, contrary to the prominence of the Nash solution under smoothing in the utility space, the entire frontier can be supported under a variety of economically-plausible perturbations. The case where the resource is multi-dimensional is qualitatively different.