Traffic scenarios are inherently interactive. Multiple decision-makers predict the actions of others and choose strategies that maximize their rewards. We view these interactions from the perspective of game theory which introduces various challenges. Humans are not entirely rational, their rewards need to be inferred from real-world data, and any prediction algorithm needs to be real-time capable so that we can use it in an autonomous vehicle (AV). In this work, we present a game-theoretic method that addresses all of the points above. Compared to many existing methods used for AVs, our approach does 1) not require perfect communication, and 2) allows for individual rewards per agent. Our experiments demonstrate that these more realistic assumptions lead to qualitatively and quantitatively different reward inference and prediction of future actions that match better with expected real-world behaviour.