  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.
