In this work, a distributed and iterative algorithm for uplink power control in the initial contention-based synchronization procedure of orthogonal frequency-division multiple access networks is derived. This is achieved by letting the mobile terminals maximize their own energy efficiency in terms of power consumption and average synchronization time exploiting a quantized feedback from the base station. The problem is formulated as a constrained finite noncooperative game in which the transmit powers are chosen from a discrete set. The theoretical solution is investigated and compared to the case of continuous powers. In addition, comparisons with existing alternatives (with or without perfect feedback) are made in terms of power expenditure, average synchronization time, and estimation accuracy.