3,582 research outputs found
Bounding the Optimal Revenue of Selling Multiple Goods
Using duality theory techniques we derive simple, closed-form formulas for
bounding the optimal revenue of a monopolist selling many heterogeneous goods,
in the case where the buyer's valuations for the items come i.i.d. from a
uniform distribution and in the case where they follow independent (but not
necessarily identical) exponential distributions. We apply this in order to get
in both these settings specific performance guarantees, as functions of the
number of items , for the simple deterministic selling mechanisms studied by
Hart and Nisan [EC 2012], namely the one that sells the items separately and
the one that offers them all in a single bundle.
We also propose and study the performance of a natural randomized mechanism
for exponential valuations, called Proportional. As an interesting corollary,
for the special case where the exponential distributions are also identical, we
can derive that offering the goods in a single full bundle is the optimal
selling mechanism for any number of items. To our knowledge, this is the first
result of its kind: finding a revenue-maximizing auction in an additive setting
with arbitrarily many goods
A Note on Selling Optimally Two Uniformly Distributed Goods
We provide a new, much simplified and straightforward proof to a result of
Pavlov [2011] regarding the revenue maximizing mechanism for selling two goods
with uniformly i.i.d. valuations over intervals , to an additive
buyer. This is done by explicitly defining optimal dual solutions to a relaxed
version of the problem, where the convexity requirement for the bidder's
utility has been dropped. Their optimality comes directly from their structure,
through the use of exact complementarity. For and it turns
out that the corresponding optimal primal solution is a feasible selling
mechanism, thus the initial relaxation comes without a loss, and revenue
maximality follows. However, for that's not the case, providing the
first clear example where relaxing convexity provably does not come for free,
even in a two-item regularly i.i.d. setting
- …