Network congestion games with player failures for charging problem of EVs via matrix approach

Abstract With the increasing popularity of electric vehicles (EVs), the congestion problem encountered during EV charging has become a new challenge that needs to be addressed. In this paper, the congestion problem of EV charging is investigated within the framework of network congestion games. It takes into account congestion during both travelling and charging stages. Initially, for the scenario where no player fails, the EV charging problem is modeled as a network congestion game, which is proven to be a potential game. Secondly, two types of games with player failures are considered. The game with player failures on roads is verified a weighted potential game, drawing support from the semi‐tensor product (STP) of matrices. The game in which players only fail at charging stations, rather than on roads, is not a (weighted) potential game but admits at least one Nash equilibrium (NE). Thirdly, the effect of player failures on NEs is discussed, and the condition that keeps the NE of the original game unchanged is provided. Finally, the theoretical results are validated through examples.