  Renewable power producers participating in electricity markets build
forecasting models independently, relying on their own data, model and feature
preferences. In this paper, we argue that in renewable-dominated markets, such
an uncoordinated approach to forecasting results in substantial opportunity
costs for stochastic producers and additional operating costs for the power
system. As a solution, we introduce Regression Equilibrium--a welfare-optimal
state of electricity markets under uncertainty, where profit-seeking stochastic
producers do not benefit by unilaterally deviating from their equilibrium
forecast models. While the regression equilibrium maximizes the private
welfare, i.e., the average profit of stochastic producers across the day-ahead
and real-time markets, it also aligns with the socially optimal, least-cost
dispatch solution for the system. We base the equilibrium analysis on the
theory of variational inequalities, providing results on the existence and
uniqueness of regression equilibrium in energy-only markets. We also devise two
methods for computing the regression equilibrium: centralized optimization and
a decentralized ADMM-based algorithm that preserves the privacy of regression
datasets.
