The global Internet has enabled a massive access of internauts to content. At the same time it allowed individuals to use the Internet in order to distribute content. This introduced new types of competition between content over popularity, visibility, influence, reputation and user attention. The rules of these competitions are new with respect to those of traditional media, and they are determined by the way resources are allocated through network protocols (such as page rank in search engines and recommendation systems that are widely spread in social networks). In this paper we first present in the introduction an overview of some central competition issues both in the Internet as well as in other types of networks. We then describe the model of when to send content in order to maximize the exposure of the content. In the two last sections we finally describe research on two bio-inspired tools that have bben used to study various competition aspects.