People often ask about difficulty in tournaments but they can be referring to troop loss or to the difficulty of the fight.
The difficulty is fixed as it is a ratio of your squad size verse the enemy. The chart below shows the ratios for the difficulty of tournaments. So it starts in your favour for the first round, is equal odds in the second round and gradually you are outnumbered until 1.6:1 in the last round. This difficulty will not change regardless of race, chapter, techs. Numbers in graph came from release notes (1.18 I believe).
What does change is the size of your squad and the cost to cater both of which are currently understood to be functions of your squad size and the tournament province number. You start round 1 with 5% of your squad size and then add that number for each round you go out. It is a linear progression so round 3 is roughly 15% and round 4 20% etc of your squad size. Here is a spreadsheet and experinced combat player on beta came up with.
https://beta.forum.elvenar.com/inde...6/&temp_hash=a70b8f454eab56470c2f8bf875e6a93d
While difficulty compared to the enemy squad size stays the same your squads size gets larger the more techs you research therefore your cost to replace troops increases. Someone determined a person who researches all optional SS techs to halflings will have double the cost in troop loss as someone who skips them all. This is a huge advantage as both players in the same chapter would have the same ability to replace troops at the same speed (not counting wonder choices/levels)
This is why the common practice now for a person keen on tournaments is to skip optional squad size techs. The tech tree is misleading for tournaments as it is opposite to provinces and the more you research SS the worse it is for tournament play. Prior to the change it was good to research the techs so those players can't undo the research and new players assume more techs makes its better and fall into a similar trap. This is why some players would prefer it to be based on max SS tech to somewhat even the "playing field" so to speak.
Catering is somehow a function of this so the cost in goods also progress in a similar fashion.