One of the main strategies to reduce GHG emissions is to trade emission allowances or permits on organised markets. Indeed, pricing CO2 encourages investments in low-carbon technologies. The design of emission trading markets is crucial to ensure their efficiency and fairness.

The authors examine the interaction between electricity generators within an oligopolistic market. They use a game-theoretical model that considers the interplay between the electricity market and the emissions market in a two-stage stochastic framework. Electricity quantities and emissions allowances are contracted in advance and committed at the futures price in a futures electricity market (first stage). Then the actual delivery of electricity and allowances occurs in a spot market (second stage). These market interactions are modelled as a game-theoretical equilibrium with both risk neutral and risk averse generators. This problem is modelled as an optimisation programme that maximises a weighted average of expected profits and the conditional value at risk thereof (CVaR), resulting in a continuous quadratically constrained quadratic problem (QCQP).

The authors use Artelys Knitro to solve this problem and to derive multiple conclusions, performing sensitivity analyses on renewable energy penetration and carbon prices for generators with different attitudes towards risk. The performance of the solver enables to consider hundreds of scenarios with varying electricity and emission allowance prices, generation costs, and level of nondispatchable renewable energy generation.