Several BBR flows do actually converge quite nicely to a fair share of bandwidth. Take a look at the presentation the guys from google gave at the IETF 97 in Seoul: https://www.ietf.org/proceedings/97/slides/slides-97-iccrg-b...

I think there is also a recording of that session somewhere on youtube.

Also, the complete paper can be downloaded for free at http://queue.acm.org/detail.cfm?id=3022184