On Quantity Competition and Transmission Constraints in Electricity Market

In this paper we characterize equilibria in a quantity game where symmetric firms face a local demand together with an export-constrained demand. Firms have unlimited access to a local demand but a restricted access to a second market, like in the electricity network where generators compete to satisfy demand but competition is restricted by transmission capacity. We show the existence of an effective demand that is continuous but not differentiable due to the transmission constraint. Three types of equilibria emerge in this context, parametrized by capacity. First, a symmetric equilibrium (unique) when the access to the second market is constrained. Second, a set of continuous and asymmetric equilibria with a fully used link but not constrained; and finally, a symmetric and unique equilibrium in which the link is not fully used. We also show how multiplicity of equilibria tends to disappear as the number of competitors increase