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In this paper, a game-theoretic framework is applied in order to model the competition scenario between high-speed rail (HSR) and airlines in the Indian context and assess the impact of speed and passengers' characteristics on the equilibrium of the game. The competition is modelled in terms of the fare and frequency offered by the operators to maximize their profits. The speed of HSR is taken as an additional strategic variable in the game with three levels of high speed: low, medium, high. A three-stage game is formulated with the entrant playing its speed strategy in the first stage followed by optimal fare and frequency selection by both the modes. Passengers are considered to be heterogeneous in nature by assuming a continuous distribution of the value of time. Numerical simulations indicate that the dominant strategy for airlines and HSR is based on accommodation and medium speed, respectively. [ABSTRACT FROM AUTHOR]