A Comprehensive Game-Theoretic Model for Electric Vehicle Charging Station Competition

En-route charging stations are essential to ensure the adoption of electric vehicles. However, careful planning is necessary due to high cost in infrastructure and potentially long waiting queues. Existing literature on the placement of charging stations largely disregards competition, sets prices to cover costs and/or disregards queues. In contrast, this work models competing station investors who aim to maximise expected profit, while electric vehicle drivers aim to minimise expected travel costs including queues. Following a game-theoretic approach, investors strategically decide station capacities, locations and charging unit power outputs as well as fees, taking into consideration building and operational costs. Given the complexity of the problem, the solution involves a combination of theoretical and algorithmic techniques to obtain subgame-perfect equilibria of investor and driver choices. Subgame-perfect equilibria are found to be at least 92.85% efficient, for reasonable fluctuations of problem parameters. Furthermore, it is found that charging prices can be up to approximately 5 times higher than marginal cost due to long charging times, and also that better charging technology may not necessarily benefit drivers in the near future. Finally, subsidies towards the purchase of charging units are shown to be beneficial for both drivers and investors, being able to generate up to 14.3% additional value than the cost of the subsidy. In contrast, subsidies on the energy price for stations are found to have small effect and can be abused by investors.