In recent years, there has been a rising concern about the policy of major search engines, and more specifically about their ranking in so-called organic results corresponding to keywords searches. The associated proposition is that their behavior should be regulated. The concern comes from search bias, which refers to search rankings based on some principle different from the expected automated relevance. In this paper, we analyze one behavior that results in search bias: the payment by content providers to the search engine in order to improve the chances to be located and accessed by a search engine user. A simple game theory-based model is presented where both a search engine and a content provider interact strategically, and the aggregated behavior of users is modeled by a demand function. The utility of each stakeholder when the search engine is engaged in such a non-neutral behavior is compared with the neutral case when no such side payment is present.