You could consider David Gurteen's Knowledge Cafe idea. I've used that once with success.
Hi I haven't run this activity, but I have been a participant.
We were told that our task was to build a village. We were split into teams and each team had to build a house for the village and was given specifications from the "project manager". At the start we were told that success was the village being completed to all the project manager's specifications by the deadline.
Well of course everyone became competitive and started working in silos rather than helping each other. There was much cheering by the team that completed their house first.
When we had all finished, we found out that each team had an incomplete set of specifications. One team knew that the windows had to be a certain size or colour, but they didn't know how high the walls had to be and vice versa.
We then had a discussion about silos, and working competitively rather than cooperatively. The goal of completing a village had been forgotten in the race for each team to win.
I even think that halfway through the "project manager" tipped us off that we needed to share information, and even then teams were trading it (I'll share x if you share y) rather than being truely collaborative!
I can't remember what we built the houses out of - probably paper and cardboard.
Hopefully this sparks some ideas that you can use.
Thank you both very helpful! Clare