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This paper considers a public transportation system, which offers Internet access services to the commuting passengers. Suppose the Internet connection is available at few roadside base stations (RSBs) in a city. Our objective is to solve the bandwidth allocation problem when there are several vehicles connected to an RSB at the same time and the bandwidth of the link to the RSB has to be shared among these vehicles. To solve this bandwidth allocation problem, we propose a game-theoretic model. The main concept of the model is to let each vehicle compete with others in order to obtain the required amount of bandwidth. We formulate this game as an auction game where the vehicles are the bidders and the RSB is the auctioneer. From the performance study, we observe that there is an equilibrium which is a solution in this game. To obtain the solution in a distributed manner, an iterative algorithm is presented.