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The entry and exit game in the electricity markets: A mean-field game approach

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    * Corresponding author
Peter Tankov and René Aïd gratefully acknowledge financial support from the ANR (project EcoREES ANR-19-CE05-0042) and from the FIME Research Initiative
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  • We develop a model for the industry dynamics in the electricity market, based on mean-field games of optimal stopping. In our model, there are two types of agents: the renewable producers and the conventional producers. The renewable producers choose the optimal moment to build new renewable plants, and the conventional producers choose the optimal moment to exit the market. The agents interact through the market price, determined by matching the aggregate supply of the two types of producers with an exogenous demand function. Using a relaxed formulation of optimal stopping mean-field games, we prove the existence of a Nash equilibrium and the uniqueness of the equilibrium price process. An empirical example, inspired by the UK electricity market is presented. The example shows that while renewable subsidies clearly lead to higher renewable penetration, this may entail a cost to the consumer in terms of higher peakload prices. In order to avoid rising prices, the renewable subsidies must be combined with mechanisms ensuring that sufficient conventional capacity remains in place to meet the energy demand during peak periods.

    Mathematics Subject Classification: 91A55, 91A13, 91A80.


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  • Figure 1.  Left: typical offer curve in the French electricity market. Right: evolution of the daily mean and standard deviation of the offers by gas-fired power plants in the French electricity market

    Figure 2.  Electricity demand projections used in the simulation

    Figure 3.  Convergence of the gain increase upon switching to the best response. The gain is given in million GBP for the entire sector

    Figure 4.  Evolution of conventional and renewable installed capacity in the three simulations. Scenario 1: renewable subsidy. Scenario 2: renewable subsidy and capacity payments for conventional plants

    Figure 5.  Evolution of the electricity price in the three simulations. Top left: peak price. Top right: peak price (zoom on the last 4 years). Bottom: base price. Scenario 1: renewable subsidy. Scenario 2: renewable subsidy and capacity payments for conventional plants

    Figure 6.  Conventional and renewable supply for peak (left graphs) and off-peak (right graphs) periods. Top: baseline scenario; middle: scenario 1; bottom: scenario 2

    Table 1.  UK Electricity installed generation capacity in 2017, GW. Conventional steam includes coal and gas. CCGT stands for combined cycle gas turbine. Wind and solar is approximately 20% solar and 80% wind, out of which there is about 60% onshore and 40% offshore. Source: UK Energy in Brief 2018

    Conventional steam CCGT Nuclear Pumped storage Wind & Solar
    18.0 32.9 9.4 2.7 40.6
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