Abstract
We study the existence and uniqueness of equilibria for perfectly competitive markets in capacitated transport networks. The model under consideration is rather general so that it captures basic aspects of related models in, e.g., gas or electricity networks. We formulate the market equilibrium model as a mixed complementarity problem and show the equivalence to a welfare maximization problem. Using the latter we prove uniqueness of the resulting equilibrium for piecewise linear and symmetric transport costs under additional mild assumptions. Moreover, we show the necessity of these assumptions by illustrating examples that possess multiple solutions if our assumptions are violated.
Highlights
We consider perfectly competitive markets upon capacitated networks, where transport costs are modeled using piecewise linear and symmetric cost functions
We prove uniqueness of market equilibria under mild assumptions
Uniqueness of market equilibria is a classical topic of mathematical economics by itself
Summary
We consider perfectly competitive markets upon capacitated networks, where transport costs are modeled using piecewise linear and symmetric cost functions. Krebs et al [16] The former proves uniqueness of long-run market equilibria using a network flow transport model as we do in our paper. The latter considers uniqueness and multiplicity of solutions in the context of short-run market models using DC power flows Both analyses do not cover transport costs, which are part of many realistic models for electricity or gas markets that consider the corresponding network infrastructure—see the literature cited above. None of these papers considers uniqueness of equilibria. We analyze perfectly competitive markets and prove uniqueness of the resulting equilibria
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