There's a problem with Tourney, at least regarding the AI building thereof. Using AIAutoplay, I found that, as France, my civ built 13 Tourneys by the year 1100. As I was under the impression that only 4 were allowed to any civ, I was very surprised... however, looking at the cities, it appears that there were only 4 made in the end, but that the building was being rebuilt multiple times (similar to how the Palace is moved when rebuilt). I'm pretty certain this was not intended.
There are several other buildings that are set up similarly to Tourney (some of the Hanseatic national wonders, I believe) so I wonder if they have the same problem.
I haven't tested whether the human player can rebuild the Tourneys multiple times, but that is likely the case... however, he wouldn't do so in most cases.
Anyhow, the AI using so much effort to build Tourneys that simply move the building to a different city is wasting a lot of effort that could go towards units or other buildings.