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Beeper vs Apple battle intensifies: Lawmakers demand DOJ investigation - Android Authority
(www.androidauthority.com)
This is a most excellent place for technology news and articles.
We're far from court cases. What we have right now is politicians asking the Department of Justice to investigate. I suspect that's more likely to go nowhere than it is to go to court.
If it did go to court, either side of the smartphone/messenger equation could be argued as anticompetitive use of market power, or both; they could claim that Apple used its market power in smartphones to popularize its messenger service, which it then used to increase its market share in smartphones.