  This paper presents models for predicted click-through rates in position
auctions that take into account two possibilities that are not normally
considered---that the identities of ads shown in other positions may affect the
probability that an ad in a particular position receives a click
(externalities) and that some ads may be less adversely affected by being shown
in a lower position than others (brand effects). We present a general axiomatic
methodology for how click probabilities are affected by the qualities of the
ads in the other positions, and illustrate that using these axioms will
increase revenue as long as higher quality ads tend to be ranked ahead of lower
quality ads. We also present appropriate algorithms for selecting the optimal
allocation of ads when predicted click-through rates are governed by either the
models of externalities or brand effects that we consider. Finally, we analyze
the performance of a greedy algorithm of ranking the ads by their expected
cost-per-1000-impressions bids when the true click-through rates are governed
by our model of predicted click-through rates with brand effects and illustrate
that such an algorithm will potentially cost as much as half of the total
possible social welfare.
