@article{KrebsScheweSchmidt2017, author = {Krebs, Vanessa and Schewe, Lars and Schmidt, Martin}, title = {Uniqueness and Multiplicity of Market Equilibria on DC Power Flow Networks}, series = {European Journal on Operations Research}, journal = {European Journal on Operations Research}, number = {271(1)}, pages = {165 -- 178}, year = {2017}, abstract = {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.}, language = {en} } @article{GrimmGruebelScheweetal.2017, author = {Grimm, Veronika and Gr{\"u}bel, Julia and Schewe, Lars and Schmidt, Martin and Z{\"o}ttl, Gregor}, title = {Nonconvex Equilibrium Models for Gas Market Analysis: Failure of Standard Techniques and Alternative Modeling Approaches}, series = {European Journal on Operational Research}, journal = {European Journal on Operational Research}, number = {273(3)}, pages = {1097 -- 1108}, year = {2017}, abstract = {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.}, language = {en} }