Abstract: The state-of-the-art technology in the field of vehicle automation will lead to a mixed traffic environment in the coming years, where connected and automated vehicles have to interact with human-driven vehicles. In this context, it is necessary to have intention prediction models with the capability of forecasting how the traffic scenario is going to evolve with respect to the physical state of vehicles, the possible maneuvers and the interactions between traffic participants within the seconds to come. This article presents a Bayesian approach for vehicle intention forecasting, utilizing a game-theoretic framework in the form of a Mixed Strategy Nash Equilibrium (MSNE) as a prior estimate to model the reciprocal influence between traffic participants. The likelihood is then computed based on the Kullback-Leibler divergence. The game is modeled as a static nonzero-sum polymatrix game with individual preferences, a well known strategic game. Finding the MSNE for these games is in the PPAD \cap PLS complexity class, with polynomial-time tractability. The approach shows good results in simulations in the long term horizon (10s), with its computational complexity allowing for online applications.