In this letter, we investigate the dynamic rate allocation and forwarding strategy adaption scheme for wireless networks with potential selfish nodes. Aided by an incentive mechanism, we develop a stochastic differential equation (SDE) to portray the dynamic node selfishness in terms of node's energy resource and incentives. Then, a stochastic optimization model is employed to maximize the average network utility while bounding the node selfishness. Based on the continuous-time Lyapunov optimization theory, we solve the optimization problem and propose a dynamic rate allocation and forwarding strategy update (DRAF) algorithm to accommodate the dynamic network state. We further analyze the tracking errors between the output of DRFA algorithm and the optimal solution. Then, an adaptive-compensation rate allocation and forwarding strategy update (ACRAF) algorithm is designed, which iterates only once when network state changes. Finally, we provide a sufficient condition that the ACRAF algorithm asymptotically tracks the moving equilibrium point with no tracking errors. Simulation results validate the theoretical analysis.