How to display a calendar with events depending on the user?

I wanted to know if there is any way to, once a user is logged in to your page (I would use some plugin to deal with this), show them a calendar that contains the events that they were added to by another user. E.g. you were invited to a party by someone and every person that was invited when they sign in to your page, they can see the event on the calendar. Does someone know how to do this?