I live in Sweden, but very early on in my career I was told that showing a competing offer would simply be viewed as "blackmailing" and you would not become very popular. I never used that tactic, instead just switching jobs.
Now the jobmarket is nothing that can be compared to the Bay area, for sure. For example many places more or less use the standard increases brokered by the union, even if you or the workplace is not unionized, with some skewing for being a high performer.
