Multiplicity of equilibria in conjectural variations models of natural gas markets

Abstract

Spatial partial equilibrium models incorporating conjectural variations are widely used to analyze the development of oligopolistic multi-agent markets, such as international energy and raw material markets. Although this model type can produce multiple equilibria under commonly used assumptions, to the best of our knowledge, the consequences for the interpretation of the model results have not yet been explored in detail. To this end, we derive a linear complementarity model for the gas market and discuss under which assumptions on the model structure a component of the solution is unique. In particular, we find that the gas flow between a trader and a consumer is unique whenever the trader is modeled to exert market power in the consumer's market. We demonstrate our findings by computing the extreme points of the polyhedral solution space and show that erroneous conclusions could be drawn whenever only one (arbitrary) point in the solution space is picked for interpretation. Furthermore, we discuss whether economically meaningful parameter value changes exist which would enforce uniqueness in all components of the solution.

European Union gas market development

“…Prices would indeed fall, because traders have no incentive to withhold gas from consumers and therefore the overall available gas increases. However, we would also see two additional effects: On one hand, lower prices increase consumption, and thus production and network congestion; On the other hand, perfectly competitive traders have no incentive to diversify consumers (Baltensperger et al [3]) and therefore are likely to ship gas to nearby markets to save transport costs, which reduces network congestion. How the combination of these effects influences the wholesale price can only be quantified by rerunning the model.…”

“…Appendix A is largely reproduced from Baltensperger et al [3]. We introduce the model equations in Appendix A.1, show an exemplary market setting with two interconnected nodes in Appendix A.2, and introduce the associated notation in Appendix A.3.…”

“…We refer to Appendix A.3 for an overview of the notation, and to ENTSO-G [15] and Baltensperger et al [3] for additional background information.…”

“…The spatial partial equilibrium model introduced by Baltensperger et al [3] is used throughout this study. The model equations and an exemplary model with two interconnected nodes are shown in Appendix A.…”

“…We assess the changes introduced by specific infrastructures by comparing pairs of simulation outcomes: SIM y,1 , SIM y,2 , and SIM y,3 are compared to SIM y,0 , while all other simulations of year y are compared to SIM y, 3 . Note that for y = 2013 we only calculated SIM y,ky+4 , since for all other simulations the corresponding reference scenario in y = 2012 could not be calculated due to lack of data.…”