TY - JOUR A1 - Krebs, Vanessa A1 - Schewe, Lars A1 - Schmidt, Martin T1 - Uniqueness and Multiplicity of Market Equilibria on DC Power Flow Networks JF - European Journal on Operations Research N2 - We consider uniqueness and multiplicity of market equilibria in a short-run setup where traded quantities of electricity are transported through a capacitated network in which power flows have to satisfy the classical lossless DC approximation. The firms face fluctuating demand and decide on their production, which is constrained by given capacities. Today, uniqueness of such market outcomes are especially important in more complicated multilevel models for measuring market (in)efficiency. Thus, our findings are important prerequisites for such studies. We show that market equilibria are unique on tree networks under mild assumptions and we also present a priori conditions under which equilibria are unique on cycle networks. On general networks, uniqueness fails to hold and we present simple examples for which multiple equilibria exist. However, we prove a posteriori criteria for the uniqueness of a given solution and characterize situations in which multiple solutions exist. KW - Market Equilibria KW - Uniqueness KW - Multiplicity KW - Networks KW - DC Power Flow Y1 - 2017 IS - 271(1) SP - 165 EP - 178 ER - TY - JOUR A1 - Grimm, Veronika A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - Uniqueness of Market Equilibrium on a Network: A Peak-Load Pricing Approach JF - European Journal of Operational Research N2 - In this paper we analyze peak-load pricing in the presence of network constraints. In our setup, firms facing fluctuating demand decide on the size and location of production facilities. They make production decisions constrained by the invested capacities, taking into account that market prices reflect scarce transmission capacities. We state general conditions for existence and uniqueness of the market equilibrium and provide a characterization of equilibrium investment and production. The presented analysis covers the cases of perfect competition and monopoly - the case of strategic firms is approximated by a conjectural variations approach. Our result is a prerequisite for analyzing regulatory policy options with computational multilevel equilibrium models, since uniqueness of the equilibrium at lower levels is of key importance when solving these models. Thus, our paper contributes to an evolving strand of literature that analyzes regulatory policy based on computational multilevel equilibrium models and aims at taking into account individual objectives of various agents, among them not only generators and customers but also, e.g., the regulator deciding on network expansion. KW - Pricing KW - Peak-Load Pricing KW - Networks KW - Uniqueness Y1 - 2017 U6 - https://doi.org/10.1016/j.ejor.2017.03.036 VL - 261 IS - 3 SP - 971 EP - 983 ER - TY - JOUR A1 - Grimm, Veronika A1 - Grübel, Julia A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - Nonconvex Equilibrium Models for Gas Market Analysis: Failure of Standard Techniques and Alternative Modeling Approaches JF - European Journal on Operational Research N2 - This paper provides a first approach to assess gas market interaction on a network with nonconvex flow models. In the simplest possible setup that adequately reflects gas transport and market interaction, we elaborate on the relation of the solution of a simultaneous competitive gas market game, its corresponding mixed nonlinear complementarity problem (MNCP), and a first-best benchmark. We provide conditions under which the solution of the simultaneous game is also the solution of the corresponding MNCP. However, equilibria cannot be determined by the MNCP as the transmission system operator's (TSO’s) first-order conditions are insufficient, which goes back to nonconvexities of the gas flow model. This also implies that the welfare maximization problem may have multiple solutions that sometimes do not even coincide with any of the market equilibria. Our analysis shows that, even in the absence of strategic firms, market interaction fails to implement desirable outcomes from a welfare perspective due to the TSO’s incentive structure. We conclude that the technical environment calls for a market design that commits the TSO to a welfare objective through regulation and propose a design where the market solution corresponds to a welfare maximum and vice versa. KW - Natural Gas Markets KW - Nonconvex Equilibrium Models KW - Uniqueness KW - Multiplicity KW - Fundamental Welfare Theorems Y1 - 2017 IS - 273(3) SP - 1097 EP - 1108 ER - TY - JOUR A1 - Krebs, Vanessa A1 - Schmidt, Martin T1 - Uniqueness of Market Equilibria on Networks with Transport Costs JF - Operations Research Perspectives N2 - 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. KW - Market Equilibria KW - Networks KW - Transport Costs KW - Uniqueness KW - Perfect Competition Y1 - 2017 IS - 5 SP - 169 EP - 173 ER -