You should not use invitations. Invitations are specifically designed to be displayed in the userβs event list. But since you do not want to spam your users, your other options (email / wall message / application) will not work either, because they inevitably lead to spam by nature ...
So, make your choice: invites - it is recommended, but there is no active notification or e-mail / wall / application - most likely, it will be considered as spam, but an active notification.
I would suggest using invitations and not worry about users being actively notified. They are recommended by Facebook, fall within their scope of the game, and even if the notification is not obvious, this method has been quite effective for most applications so far;)
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