This paper presents a human-aware collision free navigation system based on long-term motion prediction and a game against nature formulation for modelling uncertainty. The proposed approach explicitly takes into account mutual pedestrian interactions and introduces a method for estimating the confidence of predicted pedestrian reactions through the analysis of anticipated interactions in public spaces. This enables the formulation of a decision-making framework based on the minimisation of the expected value of a cost function. The effectiveness of the method proposed is demonstrated using representative simulation scenarios, showing improved safety and enhanced comfort of navigation behaviour.