Assuming immortality means you can't age but you can still be killed...
Once food and resources get too low, we'd probably start killing each other for the resources. Alliances would form. Entire communities of 'unworthy' would get slaughtered. Once the planet has been 'cleansed' so that resources stabilize, we'll do the only thing left to do, war for religious purposes.
I'll be in my underground bunker playing team fortress 2 during this entire time.