  In sponsored search, a number of advertising slots is available on a search
results page, and have to be allocated among a set of advertisers competing to
display an ad on the page. This gives rise to a bipartite matching market that
is typically cleared by the way of an automated auction. Several auction
mechanisms have been proposed, with variants of the Generalized Second Price
(GSP) being widely used in practice.
  A rich body of work on bipartite matching markets builds upon the stable
marriage model of Gale and Shapley and the assignment model of Shapley and
Shubik. We apply insights from this line of research into the structure of
stable outcomes and their incentive properties to advertising auctions.
  We model advertising auctions in terms of an assignment model with linear
utilities, extended with bidder and item specific maximum and minimum prices.
Auction mechanisms like the commonly used GSP or the well-known
Vickrey-Clarke-Groves (VCG) are interpreted as simply computing a
\emph{bidder-optimal stable matching} in this model, for a suitably defined set
of bidder preferences. In our model, the existence of a stable matching is
guaranteed, and under a non-degeneracy assumption a bidder-optimal stable
matching exists as well. We give an algorithm to find such matching in
polynomial time, and use it to design truthful mechanism that generalizes GSP,
is truthful for profit-maximizing bidders, implements features like
bidder-specific minimum prices and position-specific bids, and works for rich
mixtures of bidders and preferences.
