We propose an uplink non-cooperative game-theoretic power control algorithm for wireless data in direct sequence spread spectrum code division multiple access (DS-CDMA) single cell communication systems. We put forward a target function composed of the difference between a utility function and a pricing function. In this proposed game-theoretic algorithm, each user unilaterally and based on local information decides its transmit power level that maximizes its target function. The pricing function used is a linear function of the transmit power with a slope (pricing factor) chosen in a marketbased mechanism, where the base station (BS) decides the pricing factor and communicates it to the users in the cell. Finally, an S-modular games framework is exploited to establish the existence and uniqueness of a Nash equilibrium (NE) operating point of the proposed game. This NE operating game exhibits Pareto dominance over that of NE operating point of other existing Algorithms in the literature as we show in the simulations.