A note on the uniqueness of Nash–Cournot equilibria in an oligopolistic energy market with renewable generation and demand uncertainty

This work explores the uniqueness of Nash–Cournot equilibria in wholesale electricity markets with both thermal and renewable generation in the presence of demand uncertainty. Criteria guaranteeing a unique equilibrium are derived for an energy market where each firm owns a share of renewable generation. This work expands upon the uniqueness results proven by Lagerlöf (2006) to incorporate the presence of renewable generation into the market in the manner of Acemoglu et al. (2017). A numerical case study is used to illustrate the potential impacts of increasing renewable generation on equilibrium uniqueness and directions for future research are discussed. • Explores impact of renewable generation and demand uncertainty in a wholesale electricity market. • Generating firms own a share of a fixed amount of renewable generation. • Firms face uncertainty over the intercept parameter of a linear inverse demand function. • Sufficient conditions guaranteeing a unique Nash–Cournot equilibrium are derived. • Numerical case studies illustrate how probability distributions impact equilibrium uniqueness.