Core allocations and small income transfers

We show that, given any allocation f in the core of an exchange economy, we can find small income transfers and a Walrasian allocation f˜ relative to the transfers such that most agents are indifferent between f and f˜. In addition, we can find small income transfers and an approximate Walrasian allocation fˆ relative to the transfers such that all agents are indifferent between fˆ and f.