We provide a robust (or detail-free) strategic foundation for the Walrasian Equilibrium: a mechanism for an exchange economy with asymmetric information and interdependent values that is ex-post individually rational, incentive compatible, generates budget surplus and is ex-post nearly Pareto Efficient, when there are many agents. The level of inefficiency is proportional to the impact a single agent has on the Walrasian price. Conversely, we show that mechanisms generating smaller efficiency losses must violate some of the constraints, and so our efficiency bound is tight. The tight robust asymptotic efficiency is achieved by σ-Walrasian Equilibrium mechanisms, in which the allocation is as if each agent traded knowing all the information distributed in the economy, faced with the price that increases in the quantity traded with slope σ.