We briefly review some results from two directions of research: analyzing the complex dynamics of collaborative tagging systems, and the dynamics of sponsored search markets. The tagging presentation is based on [Halpin et al., 2007] - with some more recent results.  
The sponsored search part covers some preliminary results from a project analyzing the dynamics of advertising (sponsored) links, performed in collaboration with Sander Bothe and Han La Poutre (CWI, Amsterdam). It involves analyzing the relationships between click-through rates of different keywords, the effect of the position of the link on the click-through rate, as well as the distribution of the market share of different advertisers in such a market.


[Halpin et al., 2007] Harry Halpin, Valentin Robu, Hana Shepherd "The complex dynamics of collaborative tagging" Proc. of the 16th international conference on World Wide Web, Banff, 2007, pp.  211 - 220.