This paper proposes a cooperative power control strategy for resource adaptation in mobile network to optimize user uplink transmission power. Our approach is based on a cooperative model using the economic concepts of utility function and the random graph theory. Based on the model, we develop a distributed power control algorithm that maximizes the utilities of all mobile users. Formulating this algorithm as a cooperative strategy, we show the uncertainty and existence of the power control approach with theory of random bipartite graph and utility function. A discussion to the existence of optimal solutions is given. Then a distributed power control scheme is proposed based on the optimal solutions. It is shown by way of simulation that by introducing utility function in the power control algorithm, there is a performance improvement in terms of the utilities that mobile users obtained. Numerical results are presented for the algorithm.