  Sponsored Search Auctions (SSAs) arguably represent the problem at the
intersection of computer science and economics with the deepest applications in
real life. Within the realm of SSAs, the study of the effects that showing one
ad has on the other ads, a.k.a. externalities in economics, is of utmost
importance and has so far attracted the attention of much research. However,
even the basic question of modeling the problem has so far escaped a definitive
answer. The popular cascade model is arguably too idealized to really describe
the phenomenon yet it allows a good comprehension of the problem. Other models,
instead, describe the setting more adequately but are too complex to permit a
satisfactory theoretical analysis. In this work, we attempt to get the best of
both approaches: firstly, we define a number of general mathematical
formulations for the problem in the attempt to have a rich description of
externalities in SSAs and, secondly, prove a host of results drawing a nearly
complete picture about the computational complexity of the problem. We
complement these approximability results with some considerations about
mechanism design in our context.
