(Sports) Philosophy of Mind

Most team games have the goal of taking the ball away, and keeping it, from the opposing players. This is an incentive to reduce the participation, thus the fun, of competitors. It encourages team work on one side, but doesn't foster inclusion and rapport across the field.
As a side note for all the traditional business network builders: Golf is passive-aggressive, the players engage through the turf.
For a cooperative competition look for games where everyone gets a turn, or at least there is an incentive to give other players an opportunity to participate. Examples include tennis and role playing.