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We cast models of the generation capacity expansion type formally developed for the monopoly regime into equilibrium models better adapted for a competitive environment. We focus on some of the risks faced today by investors in generation capacity and thus pose the problem as a stochastic equilibrium model. We illustrate the approach on the problem of the incentive to invest. Agents can be risk neutral or risk averse. We model risk aversion through the CVaR of plants' profit. The CVaR induces risk-adjusted probabilities according to which investors value their plants. The model is formulated as a complementarity problem (including the CVaR valuation of investments). An illustration is provided on a small problem that captures several features of today's electricity world: a choice often restricted to coal and gas units, a peaky load curve because of wind penetration, uncertain fuel prices, and an evolving carbon market. We assess the potential of the approach by comparing energy-only and capacity market organizations in this risky environment. Our results can be summarized as follows: a deterministic analysis overlooks some changes of capacity structure induced by risk, whether in the capacity market or energy-only organizations. The risk-neutral analysis also misses a shift towards less capital-intensive technologies that may result from risk aversion. Last, risk aversion also increases the shortage of capacity compared to the risk-neutral view in the energy-only market when the price cap is low. This may have a dramatic impact on the bill to the final consumer. The approach relies on mathematical programming techniques and can be extended to full-size problems. The results are illustrative and may deserve more investigation.

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In the real world two classes of market designs are implemented to trade electricity in transmission constrained networks. Analytical results show that in two node networks integrated market designs reduce the ability of electricity generators to exercise market power relative to separated market designs. In multi node networks countervailing effects make an analytic analysis difficult.We present a formulation of both market designs as an equilibrium problem with equilibrium constraints. We find that in a realistic network, prices are lower with the integrated market design.

Following the development of decentralized production technologies, energy communities have become a topic of increased interest. While the potential benefits have been described, we use the framework of cooperative game theory to test the ability of such communities to adequately share the gains. Indeed, despite the potential value created by such coalitions, there is no guarantee that they will be viable: a subset of participants may find it profitable to exit the community and create another one of their own. We take the case of a neighborhood, having access to a limited resource e.g. a shared roof or piece of land which they can exploit if they invest in some renewable production capacity. By joining the community, participants also enjoy aggregation gains in the form of reduced network fees. We find conditions depending on the structure of renewable installation costs, on the magnitude of the aggregation effect and coordination costs and, most importantly, on the chosen sharing rule, under which the whole energy community is stable. Efficiency could require the intervention of a social planner or a change in network tariff structures.