  We study the mechanism design problem of selling $k$ items to unit-demand
buyers with private valuations for the items. A buyer either participates
directly in the auction or is represented by an intermediary, who represents a
subset of buyers. Our goal is to design robust mechanisms that are independent
of the demand structure (i.e. how the buyers are partitioned across
intermediaries), and perform well under a wide variety of possible contracts
between intermediaries and buyers.
  We first study the case of $k$ identical items where each buyer draws its
private valuation for an item i.i.d. from a known $\lambda$-regular
distribution. We construct a robust mechanism that, independent of the demand
structure and under certain conditions on the contracts between intermediaries
and buyers, obtains a constant factor of the revenue that the mechanism
designer could obtain had she known the buyers' valuations. In other words, our
mechanism's expected revenue achieves a constant factor of the optimal welfare,
regardless of the demand structure. Our mechanism is a simple posted-price
mechanism that sets a take-it-or-leave-it per-item price that depends on $k$
and the total number of buyers, but does not depend on the demand structure or
the downstream contracts.
  Next we generalize our result to the case when the items are not identical.
We assume that the item valuations are separable. For this case, we design a
mechanism that obtains at least a constant fraction of the optimal welfare, by
using a menu of posted prices. This mechanism is also independent of the demand
structure, but makes a relatively stronger assumption on the contracts between
intermediaries and buyers, namely that each intermediary prefers outcomes with
a higher sum of utilities of the subset of buyers represented by it.
