Non-Manipulability of Walrasian Mechanisms in Economies with a Large Number of Objects

We consider a problem of allocating multiple identical objects to a group of agents and collecting payments. Each agent may receive several objects and has quasi-linear preferences with a submodular valuation function. It is known that Walrasian mechanisms are manipulable. We investigate the incentive property of Walrasian mechanisms in economies with a large number of objects. Given a set of agents and a preference profile, an agent i asymptotically dominates an agent j if at sufficiently many objects, i's incremental valuation is higher than j's incremental valuation. We show that for each economy, if there is no agent asymptotically dominating the other agents, and if there are sufficiently many objects, any Walrasian mechanism is non-manipulable at the economy. We also consider replica economies, and show that for each economy, if it is replicated sufficiently many times, the minimum price Walrasian mechanisms are non-manipulable at the replica economy.