<p>This work analyses the impact of incorporating risk measures such as conditional value-at-risk, (second-order) stochastic dominance constraints, and a concave utility function, into equilibrium energy markets. It defines two illustrative problems, with price-making firms facing stochastic demand and stochastic costs respectively, and derives risk-averse equilibrium models based upon these problems. Analytic and numeric results from these models are discussed, highlighting how risk aversion leads to modified expected prices and profits. Specific attention is paid to how the risk measures compare to each other, and how their incorporation alters the complexity of the problem. The problems are defined as mixed complementarity problems using the Karush-Kuhn-Tucker conditions, and the potential to recast them to equivalent convex optimization problems is detailed. The work conducts a numerical analysis of the models to gauge the computational expense associated with each risk measure. The impact of incorporating risk measures into equilibrium energy markets is hitherto underexplored in the literature, as are comparative analyses of the various risk measures and their respective advantages in terms of applicability and computational cost. The results indicate that risk aversion causes the variability of profits to decrease regardless of the chosen measure, and highlight the influence which hedging instruments have on risk averse players and price dynamics. They additionally demonstrate that CVaR has a significantly higher computational cost than other risk measures. With increasing stochasticity in energy markets owing to the transition to renewables and geopolitical turmoil, it is imperative that models account for risk-averse decision making accurately, and that the impact of risk measures is understood—this work addresses this gap.</p>