A difference between Powered Two Wheelers (PTW) drivers’ behavior and other drivers’ behavior in urban arterials is the frequency of overtaking. The present paper focuses on PTW overtaking and models the specific behavior using concepts of Game Theory. Both the PTW driver and the lead vehicle’s driver are assumed rational decision-makers that develop strategies, trying to maximize their payoffs. These strategies may be cooperative or not with respect to the distances and safety gaps and other behavioral aspects. The payoff function is formulated based on a novel latent statistically determined driving indicator, which quantifies both the driving risk and comfort. The proposed model is evaluated using trajectory data from video recordings on an urban arterial. Results show that both drivers have maximized gains by following a cooperative strategy. Findings also reveal that the successful overtaking rate is higher, when the PTW driver is non-cooperative, whereas lower overtaking rates occur, when the driver of the lead vehicle is non-cooperative. Finally, the concepts of Dominant Strategies, bounded rationality and the construction of the optimum payoff function are further discussed.