We characterise the set of dominant strategy incentive compatible (DSIC),
strongly budget balanced (SBB), and ex-post individually rational (IR)
mechanisms for the multi-unit bilateral trade setting. In such a setting there
is a single buyer and a single seller who holds a finite number k of identical
items. The mechanism has to decide how many units of the item are transferred
from the seller to the buyer and how much money is transferred from the buyer
to the seller. We consider two classes of valuation functions for the buyer and
seller: Valuations that are increasing in the number of units in possession,
and the more specific class of valuations that are increasing and submodular.
Furthermore, we present some approximation results about the performance of
certain such mechanisms, in terms of social welfare: For increasing submodular
valuation functions, we show the existence of a deterministic 2-approximation
mechanism and a randomised e/(1-e) approximation mechanism, matching the best
known bounds for the single-item setting