A three-stage market-game mechanism is devised that is simple (actions are quantities and outcomes are determined by arithmetic operations that do not depend on details of the economy) and achieves efficiency in a two-divisible-good, pure-exchange setting with potential information-aggregation. After an entry stage, agents make offers which are provisional for all but a small, randomly selected group. Then, those offers are announced, and everyone else makes new offers with payoffs determined by a Shapley-Shubik market game. For a finite and large number of players, there exists an almost ex post efficient equilibrium. Conditions for uniqueness are also provided.