Sponsored search has grown to be an important share of the advertisement market and a major income source for large Internet companies. Its success relies not only on the explosive Internet use but also on successful implementation that made it a highly efficient and profitable concept for advertisers and search engines, in particular, through the use of keyword auctions. Up until now, most of the research relies on the simplest game-theoretic models to extract useful results. We extend the most common models to encapsulate an aspect of the system that only recently has begun to draw...