Team building activity for semi distributed team
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I am part of a larger IT team that is effectively split up into 3 teams of about 25 people each.  Each team is located thousands of miles away from the other teams, yet we have to work closely together.

In order to improve team spirit, we are planning to have a global IT team building activity.

The activity will be virtual, through video conferencing (let's assume we have a technical infrastructure to support any kind of video/virtual conferencing), and has to have the following concepts/aspects : 

- people have to feel as if they're playing a game (this can be because they actually ARE playing a game)
- there has to be a competitive element, either individually (but it is a very large group), or between the geographical teams
- it has to be time boxed to a duration of 2 hours.  shorter is definitely an option, longer is impossible because of time zone differences
- ideally, the game/event should allow or even force all individuals (and not just the talkative/active ones) to take part, so everyone can get to know everyone (at least a little bit)

I'm looking for idea's, concepts, experiences, existing games (board games, video games, ...) that would fit into this activity.

The biggest challenge for an event like this seems to be the size of the teams.  By having 3 large teams in one video conference, it might quickly turn into a chaotic mess.