Channel allocation was extensively studied in the framework of cellular networks. But the emergence of new system concepts, such as cognitive radio systems, has brought this topic into the focus of research again. In this paper, we study in detail the problem of competitive multi-radio multi-channel allocation in wireless networks. We study the existence of Nash equilibria in a static game and we conclude that, in spite of the non-cooperative behavior of such devices, their channel allocation results in a load-balancing solution. In addition, we consider the fairness properties of the resulting channel allocations and their resistance to the possible coalitions of a subset of devices. Finally, we present three algorithms that achieve a load-balancing Nash equilibrium channel allocation; each of them using a different set of available information.