In this paper, we consider the selfish routing problem in non- cooperative wireless mesh networks where the capacity can be improved by transmitting over multiple radios simultaneously using orthogonal channels. The problem is that there are some agents who are in charge of their transmissions and each of them is selfish to minimize its own transmission cost without considering the overall performance of the network. But the embarrassment in wireless mesh networks is that the selfish agents perhaps may cause interference for the non-cooperation. We think that the game theoretic tools are helpful for the selfish agents to make feasible choices. We yield a sufficient condition of the existence of pure strategy Nash equilibrium in our
Strong Transmission Game
and prove it in this paper. Some simulations reveal the feasibility of our game theoretic approach.