Channel allocation has been extensively studied in the framework of cellular networks, but the emergence of new system concepts, such as cognitive radio systems, bring this topic into the focus of research again. In this paper, we provide a formal analysis of the selfish multi-radio channel allocation problem using game theory. We conclude that in spite of the non-cooperative behavior of such devices, their channel allocation results in a Pareto- and system-optimal solution. Furthermore, we present a simple algorithm to achieve this efficient channel allocation. To the best of our knowledge, our paper is the first contribution to this important topic.