Games rely too much in the player defeating an enemy. We need more games without any kind of adversary to be defeated. Imagine for example a game were the players are stranded in an island. The objective is to all players too survive till rescue arrive. they need to get food, water, shelter and generally keep healthy. Things like hunger, thirst and exposition to the elements will deplete their health. Since all players need to survive, they need to share resources and help each other. It would be a game I would love to play.
But knowing people, I am pretty sure a lot of people would have fun just screwing around the other players and that is that. But maybe is just because games don't explore that much cooperation and focus in competitiveness.