Every week (starting Tuesday to be specific) a new tournament begins. Initially, you might not see a benefit to participating in the tournament. Doesn’t provide relics for your boosted goods, uses coins and supplies and goods to cater, takes fighting units, etc…
However, there is one benefit that everyone can enjoy from every tournament…
And that is fast and easy Knowledge Points.
Typically the first couple of tournaments are close to your city. These tournaments are very cheap to cater, perhaps a couple hundred level one and/or level two goods for each battle. In less than a minute of clicking and catering you can get through the entire tournament. The larger cities do have an advantage here due to more goods availability.
Normally the first two tournaments provide 4 knowledge points and 4 relics per battle. Even if the relics are not a boosted good for you, they can be used to create spells in your Magic Academy or for upgrading certain Wonders.
When the closest two tournaments are in their second round the benefits go up. Once you get beyond the first two tournaments, the benefits go down and the costs go up (you are at a further distance from your city).