Well actually, that's theoretically possible to run a "server" without a real machine
If you declare to a master server, "There, i have a server xabc" and the master server itself will get the "i wanna join xabc lulz! Put me on players list" and keep a list of players, but it's the players all together who maintain the game up(using a P2P technology), you will have a server with no machine behind it, apart from the playing players
In practice, well, a game will need a "impartial authority" otherwise all the clients would be like "i hit u!" "no u lulz!" "hey u got kicked already" "never lulz!"
that's why this doesn't exist...that's part of the anarchy idealism
What's possible, on this technology, is to have that "regulating authority", as a server running all the time, which says, "hey, that guy got kicked, don't send the game info to him", or "Yes, You scored a hitand killed him"