I play alot more SP than MP demigod. For this reason, the tournament mode has been the most fun for me. The issue is that playing tournament on normal difficulty is especially easy, while on hard it is near impossible.
In normal difficulty, I think I could win every game just by sitting back and watching. The bonuses are very strong on your side, and quite weak for the AI. We get rich very quickly, gain Exp very quickly, have more HP, etc. Play for 5 minutes, look at the scoreboard, and the difference is obvious. Playing the tournament on normal has no challenge.
On hard, the next step up from normal, things are COMPLETELY different. The money and exp you get are tremendously lower. The enemy is much, much tougher. I can try very, very hard to play a good game, but my side's penalties and the enemy's bonuses are just too lopsided. As above, looking at the scoreboard after 5 minutes shows the enemy always has several exp. levels above ours, few if any enemy have died, and many of my side's demigods have died.
If I didn't know which difficulty I had picked, I would say that normal is easy, and hard is impossible. I think there really needs to be a middle ground here. I can't imagine playing the tournament on easy or impossible modes, with how lopsided normal / hard already is.
SP tournament mode is a great concept and I enjoyed playing through it in the beginning, but now due to lack of challenge / impossibility, respectively, I don't play SP anymore. I would really like to see a future patch that adjusts the penalties / bonuses in the tournament to dampen this drastic lopsidedness; put some challenge into normal difficulty, and soften the disparity on hard. If this was done, I would be playing SP demigod again.