Multiplicity of equilibria in conjectural variations models of natural gas markets

TL;DR

This paper investigates the multiple equilibria in conjectural variations models of natural gas markets, highlighting the importance of understanding solution multiplicity for accurate market analysis and interpretation.

Contribution

It derives a linear complementarity model for the gas market and identifies conditions under which solution components are unique, revealing potential pitfalls in interpreting single solutions.

Findings

Gas flow between trader and consumer is unique under certain market power assumptions.

Multiple equilibria can exist in the model, affecting interpretation of results.

Erroneous conclusions may arise from analyzing only one solution point.

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.