Information aggregation in a large multi-stage market game

A two-stage market-game mechanism is devised that is both simple (agents' actions are quantities and outcomes are determined by simple algorithms that do not depend on the details of the economy) and achieves efficiency in a two-divisible-good, pure-exchange setting with potential information-aggregation. First, agents make offers, which are provisional for all but a small, randomly selected group. Then, those offers are announced, and everyone else gets to make 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.