The raising complexity in distributed embedded systems makes it necessary that the communication of such systems organizes itself automatically. In this paper, we tackle the problem of sharing bandwidth on priority-based buses. Based on a game theoretic model, reinforcement learning algorithms are proposed that use simple local rules to establish bandwidth sharing. The algorithms require little computational effort and no additional communication. Extensive experiments show that the proposed algorithms establish the desired properties without global knowledge or a priori information. It is proven that communication nodes using these algorithms can co-exist with nodes using other scheduling techniques. Finally, we propose a procedure that helps to set the learning parameters according to the desired behavior. Therefore, we prefer to approach the goal of a working communication system from a different perspective. Starting with minimal constraints on the individual communication nodes, the nodes themselves should be able to establish communication. This should be done by using simple local rules with as less global information as possible. As the first step in this development process, we want to take a look at bandwidth-constrained communication, where the quality of the function varies with the used amount of bandwidth. In future work, these constraints will be extended to cover a larger field of applications.The remainder of the paper is organized as follows. In Section 2 the problem is defined and placed into the context-related work. In Section 3, the priority-based medium access game is formulated, which represents the fundamentals for the proposed methods. Section 4 presents the distributed reinforcement learning algorithm to establish fair bandwidth distribution. The parameters are analyzed and it is proven that the algorithm also works together with other scheduling methods. In Section 5, the period access scheme is introduced and analyzed, while Section 6 concludes our work and gives outlook on future work.