St-Hot: A Prospect of Price Equilibrium in a Multi-Player Game for Electric Vehicle Charging Application

Abstract

This article studies a game theory-based pricing competition among multiple non-cooperative electric vehicle charging stations (EVCS) that seek to maximize expected profit. In contrast, electric vehicle (EV) drivers aim to minimize charging costs. In this regard, we introduce a modified game setup that alleviates the limitations of a conventional Hotelling’s game (CHG) application to achieve the price equilibrium among multiple non-cooperative players in a discrete dynamic market. In a CHG, it is assumed that each player has a positive market share. However, a CHG provides positive utilities to all players at Nash equilibrium (NE) only if they choose prices that satisfy the market sharing condition (MSC). The NE price depends on the players’ locations. Therefore, positive utilities can be achieved only if the players’ locations are confined such that the resultant NE price satisfies the MSC. The proposed game is called the St-Hot (Stackelberg-Hotelling), which can be applied to achieve the price equilibrium for those locations of players where the CHG fails to satisfy the MSC. The proposed game is applied in an EV charging environment, wherein multiple competitive EVCSs are placed at strategic locations in a linear space. The equilibrium condition is analyzed using closed-form solutions, and the results are compared with the existing CHG model. The analysis reveals that every EVCS remains profitable in a competitive market, irrespective of their location. This demonstrates that the proposed game model ensures profitability for each EVCS, showcasing its superiority over CHG.

Keywords

• Charging station
• competition
• electric vehicle
• game-theory
• Hotelling’s law
• Nash equilibrium (NE)