The peak-load pricing literature analyzes investment incentives in industries where demand is fluctuating and storability of the output is limited; see [6] for an overview. In such an environment firms will find it optimal to invest in a differentiated portfolio of base- and peakload technologies. For the case of perfectly competitive markets, the unique equilibrium of this game is welfare optimal, i.e., firms take the right investment and production decisions. The approach of peak-load pricing is currently extensively used to analyze electricity markets, e.g., by [34] or [31], and many others. The scope of this paper is to extend existence and uniqueness results of the peak-load pricing literature to the case where producers and consumers interact on a network. This is an important contribution to the literature on liberalized electricity markets, where typically private firms decide on investment and production, guided by incentives from spot market trading. In such an environment an adequate model of peak-load pricing on a network must account for the network constraints that the agents face at the spot markets whenever they are reflected in the spot market prices. One of the results of our analysis is that the consideration of network constraints in a model of peak-load pricing does not require additional assumptions to guarantee uniqueness of the equilibrium. That means, all assumptions on cost and demand functions that guarantee a unique solution in the absence of network considerations will always guarantee uniqueness when also considering network constraints. The ability to establish a unique solution of this game is a prerequisite to meaningfully analyze complementary decisions taken by other agents—such as the regulator’s decisions on network expansion or the regulatory framework itself; see e.g., the analysis in [21]. In this paper we propose a framework that captures trading at spot markets, where market prices reflect scarce network capacities. Demand at each node is fluctuating. We analyze a setup where firms decide on size and location of production facilities and make production decisions that are constrained by the invested capacities, taking into account regionally differentiated prices reflecting network constraints. We provide general conditions that allow to establish uniqueness of the resulting market equilibrium under perfect competition, characterize this equilibrium, and provide an intuitive example. In an extension we show that our results still hold if strategic behavior of firms is approximated based on the conjectural variations approach, analogously to the approach chosen, e.g., by [43].