It would use tickets as entry fee for those who don’t own Illuvials. Tickets can be earned from game play or bought etc.
All Illuvial levels and stats are standardized at beginning.
When you own an Illuvial you can upgrade from standard stats/levels to its stats/levels during game play. This gives the opponent credits in equivalent amount to perform their own Illuvial upgrades, even if they don’t own the Illuvial. They can also use the credits for augments or save them for the next battle etc.
The winner gets the tickets plus ILV reward points, if they owned Illuvials and used them during gameplay. Basically credits generated from using owned Illuvials converted into ILV points.
Non-owner winners only get their ticket back and possibly the tickets from the other non-owner opponent. They can then sell the tickets or use them for the next battle.
This encourages owning Illuvials with good stats and levels, while still creating a level playing field for those without Illuvials or low stats/level Illuvials.
We can therefore match players ranging from owning 0 Illuvials to those with all perfect stats/level Illuvials and those who don't own Illuvials enjoy the nice temporary credits during their gameplay.
This gives Illuvials with not so perfect power much needed utility and makes gameplay way more interesting for Ranked players.
F2P players can play Ranked and experience the benefits from ownership just by playing against someone who owns (because they get credits).
It also encourages levelling up your Illuvials and adding more and more to your Illuvial set. It basically fills the huge gap between owning nothing and a full set of perfect Illuvials.