Traditional cognitive radio spectrum allocation algorithms tend to ignore the influence of transmission power on network interference and have the drawback of high interaction cost between nodes. In response to these problems

by quantifying transmission power levels

we formulate the channel assignment and power control problem as a distributed non-cooperative game

in which each second user's purpose is to maximize the elastic traffic rewards. Formally

the formulated game is proved to be an exact potential game and converges to Nash equilibrium (NE) point. Furthermore

introducing the stochastic learning theory into game model

we propose a strategy selection algorithm based on stochastic learning

then the sufficient condition and strict proof for the convergence of this algorithm to pure strategy NE point are given. Finally

Simulation results show that the proposed algorithm can achieve high system throughput and improve users' satisfaction with a small amount of interactions.