We propose a new algorithm for distributed power control in cellular communication systems. We define a cost for each mobile that consists of a weighted sum of power and square of signal-to-interference ratio (SIR) error and obtain the static Nash equilibrium for the resulting costs. The algorithm requires only interference power measurements and/or SIR measurements from the base station and converges even in cases where limits on available power render the target SIRs unattainable. Examples generated using realistic data demonstrate that, in demanding environments, the Nash equilibrium power provides substantial power savings as compared to the power balancing algorithm while reducing the achieved SIR only slightly. Additional simulations show that the benefit of the Nash equilibrium power control over the power balancing solution increases as the receiver noise power or number of users in the cell increases. The algorithm has the advantage that it can be implemented distributively. An additional benefit of the algorithm is that, based on their chosen cost function, mobiles may choose to "opt out", i.e., stop transmitting, if they determine that the power required to achieve their SIR objectives is more expensive to them than not transmitting at all.