Radio interfaces and channels are two sorts of resources in a multi-channel, multi-radio wireless mesh network. An efficient allocation of radio resources to mesh devices should reduce co-channel interference for higher throughput while maintaining network connectivity. Unlike much research effort on such optimization dealing with link-or higher-level interference, this study is concerned with physical-layer interference. We propose a two-stage radio allocation scheme. The first stage assigns channels to radios using a game-theoretic approach while the second stage assigns the resulting radio-channel pairs to links using a greedy method. In the proposed game, wireless interfaces are modeled as players participating in a radio resource game with a utility function defined to minimize co-channel interference from other players. We prove that the game eventually reaches a pure-strategy Nash equilibrium regardless of the game's initial configuration. Simulation results indicate that the proposed scheme leads to more operative links than previous methods.