This paper presents a game theoretic decision making process for autonomous vehicles. Its goal is to provide a solution for a very challenging task: the merge manoeuvre in high traffic scenarios. Unlike previous approaches, the proposed solution does not rely on vehicle-to-vehicle communication or any specific coordination, moreover, it is capable of anticipating both the actions of other players and their reactions to the autonomous vehicle's movements. The game used is an iterative, multi-player level-k model, which uses cognitive hierarchy reasoning for decision making and has been proved to correctly model human decisions in uncertain situations. This model uses reinforcement learning to obtain a near-optimal policy, and since it is an iterative model, it is possible to define a goal state so that the policy tries to reach it. To test the decision making process, a kinematic simulation was implemented. The resulting policy was compared with a rule-based approach. The experiments show that the decision making system is capable of correctly performing the merge manoeuvre, by taking actions that require reactions of the other players to be successfully completed.