In recent years, there has been a rising concern about the policy of major search engines. The concern comes from search bias, which refers to the ranking of the results of a keyword search on the basis of some other principle than the sheer relevance. This search bias is also named search non-neutrality. In this paper, we analyze one non-neutral behavior, that is, a behavior that results in a search bias: the payment by content providers to the search engine (aka. side payment) in order to improve the chances to be located and accessed by a user. A game theory-based model is presented where a search engine and two content providers interact strategically, while the aggregated behavior of users is modeled by a demand function.The utility of each stakeholder (i.e., the users, the search engine, and each content provider) when the search engine is engaged in such a non-neutral behavior is compared with that of the neutral case, when no such side payment is present.Additionally, the paper analyzes the organization of such an industry, specifically, the search engine and content providers incentives for a partial and full merger with the content providers, and the effects of each organization on the users. This paper concludes by identifying the circumstances under which the search bias, on the one hand, and the integration, on the other, will effectively result in the users being harmed. This eventual harmful situation will provide a rationale for regulatory measures to be adopted.