With an effort to allocate divisible resources among suppliers and consumers, a double-sided auction model is designed to decide strategies for individual players. Under the auction mechanism with the Vickrey-Clarke-Groves-type payment, the incentive compatibility holds, and the efficient bid profile is a Nash equilibrium (NE). However, it brings difficulties for players to implement the efficient solution due to the fact that there exist infinite number of NEs in the underlying double-sided auction game. To overcome this challenge, we formulate the double-sided auction game as a pair of single-sided auction games which are coupled via a joint potential quantity of the resource. A decentralized iteration procedure is then designed to achieve the efficient solution, where a single player, a buyer, or a seller implements his best strategy with respect to a given potential quantity and a constraint on his bid strategy. Accordingly, the potential quantity is updated with respect to iteration steps as well. It is verified that the system converges to the efficient NE within finite iteration steps in the order of O(ln(1/epsilon)) with epsilon representing the termination criterion of the algorithm.