This work aims at providing an energy-efficient perspective to the problem of contention-based synchronization in (orthogonal) frequency-division multiple-access communication systems. This is achieved by modeling the terminals and their corresponding receivers at the base station as economic and rational agents that engage in a noncooperative game, in which each one trades off its available resources so as to selfishly maximize its own revenue (in terms of probability of code detection) while saving as much energy as possible. Quality-of-service requirements given in terms of probability of false alarm and timing estimation accuracy are added to the problem formulation. The existence and uniqueness of the Nash equilibrium of the game are studied. An iterative and distributed algorithm based on best-response dynamics (at the transmit side) and a practical parameter estimation (at the receive side) are proposed to achieve the equilibrium point. Numerical results are used to evaluate the performance of the proposed solution in terms of power consumption, average synchronization time and estimation accuracy and to make comparisons with existing alternatives.