  A Lookahead Auction (LA), introduced by Ronen, is an auction format for the
sale of a single item among multiple buyers, which is considered simpler and
more fair than the optimal auction. Indeed, it anonymously selects a
provisional winner by a symmetric ascending-price process, and only then uses a
personalized posted price. A LA auction extracts at least 1/2 of the optimal
revenue, even under a correlated value distribution. This bound is tight, even
for 2 buyers with independent values. We introduce a natural extension of LA,
called lookahead with pooling (LAP). A LAP auction proceeds as LA, with one
difference: it allows the seller to pool together a range of values during the
ascending-price stage, and treat them the same; thus, it preserves the
simplicity and fairness of LA. Our main result is that this simple pooling
operation improves the revenue guarantees for independent buyers from 1/2 to
4/7 of the optimal revenue. We also give a complementary negative result,
showing that for arbitrary correlated priors LAP cannot do better than 1/2
approximation.
