See [1], section "Number of competitors", page 12. This isn't a policy document, but an EU study. An interesting result in that paper is that low interest rates make tacit collusion more profitable. We've been in a period of very low interest rates for some time now, which increases the number of competitors for whom tacit collusion pays.

As before, collusion is sustainable if and only if firms put a sufficient weight on future profits. The critical threshold for the discount factor, δ, now depends on the number of firms: the more competitors there are, and the higher this threshold, meaning that collusion is less and less sustainable. For example, the threshold increases from 1/2 = 0.50 to 1/3 = 0.67 when the number of competitors increases from 2 to 3. This means that if the firms’ discount factor lies around 0.60, say, two “competitors” could in fact maintain the monopoly outcome but three or more competitors would have to price at cost.

[1] http://ec.europa.eu/competition/mergers/studies_reports/the_...