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Uniqueness of Market Equilibria on Networks with Transport Costs

Vanessa Krebs (vanessa.krebs***at***fau.de)
Martin Schmidt (mar.schmidt***at***fau.de)

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.

Keywords: Market Equilibria, Networks, Transport Costs, Uniqueness, Perfect Competition

Category 1: Applications -- OR and Management Sciences

Category 2: Network Optimization

Category 3: Convex and Nonsmooth Optimization


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Entry Submitted: 11/22/2017
Entry Accepted: 11/22/2017
Entry Last Modified: 04/24/2018

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