I know peer reviewing is done freely and voluntarily, at least I think for the most part, so I am not sure strike is the best way of calling it, but it gives the idea. With all the recent discussion about open access and overworked researchers that relate to the publishing cycle, I was wondering if there has been any protest, or strike, or talks for a strike by peer reviewers.
Not en masse. If researchers refused to review en masse, the system would break down and no papers would be published (or they'd be published without review) and the impact would be very visible.
On smaller scales there has been a Cost of Knowledge boycott of Elsevier, an individual publishing house. This was initiated by Timothy Gowers in 2012, in protest of Elsevier's perceived high prices and gross margins. The target is Elsevier because it is the "worst offender" - Elsevier's margins are very high, above 20%. The boycott allows the signatories to say if they're not willing to publish with, to do editorial work, or to referee for Elsevier. It's had minimal impact: as of time of writing, there are 16,946 signatories, a tiny fraction of the number of academics in the world (millions). It did, however, lead to Elsevier lowering its prices slightly for mathematics journals as well as making some old papers available for free.
On an even smaller scale, I've seen researchers decline to review papers because they don't review for non-OA journals, or because they don't work for free. This is a very small fraction however: I've invited hundreds of reviewers, and the number who decline for these reasons can be counted on one hand.
Researchers have refused to review for Elsevier, as part of the Cost of Knowledge boycott, which
- Objects to exorbitantly high prices; and
- Objects to measures that restrict free information.
The initial success of the boycott was summarised in 2014 by Sir Timothy Gowers (Fields Medal recipient):
A little over two years ago, the Cost of Knowledge boycott of Elsevier journals began. Initially, it seemed to be highly successful, with the number of signatories rapidly reaching 10,000 and including some very high-profile researchers, and Elsevier making a number of concessions, such as dropping support for the Research Works Act and making papers over four years old from several mathematics journals freely available online. It has also contributed to an increased awareness of the issues related to high journal prices and the locking up of articles behind paywalls.
Apart from the Cost of Knowledge, which was a while ago now and had a broader scope than just reviewing, more recently there was No Deal No Review by Finnish researchers. They boycotted the task of peer reviewing for traditional publishers in order to put pressure on them while they negotiated with the Finnish universities.
We have recently launched an initiative which is very similar to what you ask about: No free view? No review!. This allows researchers to pledge that they will not do reviewing work for venues that do not put their research in open access. It is not specifically targeted to one single publisher or research field.
Disclaimer: I'm one of the people behind the initiative.
Another similar existing initiative is Research Without Walls.