Conjecture on why equilibrium demand remains positive in the Italian day-ahead market case study

Prove or refute the conjecture that, in the Italian day-ahead electricity market instance analyzed (October 24, 2024 at 8 pm), regional demand and supply are sufficiently balanced to ensure that the Nash equilibrium net consumptions z_j are positive in every market, despite the Walrasian-welfare positivity condition j(0)=a of Theorem 4 not being satisfied.

Background

The paper establishes a sufficient condition (Theorem 4) for non-negativity of market net consumption z when all inverse demand functions share a common intercept, i.e., _j(0)=a for all markets. In the Italian case study, the authors calibrate affine inverse demand and quadratic cost functions from real bids and transit limits; this calibration does not satisfy the identical-intercept condition.

Despite the violation of the sufficient condition, the computed equilibrium shows positive demand in each market. The authors explicitly conjecture that the observation is due to a balance between regional demand and supply that avoids anomalous behaviors, and they highlight this as an unresolved point in the empirical setting.

References

The demand at equilibrium in each market is positive, even though the hypothesis of Theorem \ref{theo:pos} is not satisfied. Our conjecture is that, in this real world example, the demand and the supply in each region are sufficiently balanced to avoid anomalous behaviors.

— Equilibria in Network Constrained Markets with Market Maker  (2501.00191 - Como et al., 2024) in Section 5 (A case study), final bullet list comparing model predictions with GME data