Paradox/Companions

Companions are Characters that have decided to join Luka on his journey.

Recruitment
Companions are primarily added by defeating enemies in combat. After every victory, there is a chance of them asking to join Luka which can be accepted or declined. The formula seems to be

(Affinity)*(Recruitment Chance)*(Recruitment Rate) = (Join Chance)

Let's look at an example.

Dahlia has low recruitment chance, 1/16, so let's do everything to increase our chances. We raise her Affinity to 100 and we get 300% Recruitment Rate, the max for Part 1, and plug these numbers into the Formula.

(100)*(1/16)*(300/100) and let's simplify that to (100/16)*3.

100 divided by 16 to give us 6.25 which is then multiplied by 3 to give us 18.75. In other words, she has a little less than a 20% chance to ask to join at the end of every victory against her.

Some unique characters have special circumstances to be recruited, regardless of Affinity, Recruitment Chance, and Recruitment Rate. It can as simple as challenging to a battle, or it could be through story progression such Ilias or Alice, events such as Lime, quests such as Amira, and other conditions. Some companions force their way into the party like Sonya.

Benefits
Luka can travel with up to seven Companions with him at any given time. All other companions are stored in the PC, the Monster Lord's Pocket Castle. Four members of the party can be active in combat at any given time with another four in reserve and can be switched at any times when not in battle and at the start of every turn in battle, unless the party is disabled by Status Effects. While anyone can learn any Job, Companions may have a variety of races among them with different benefits for combat. Additionally, each Companion has a Unique Trait that gives them special passive bonuses.

Out of combat, Companions have both practical and personal benefits. At high Affection values, Companions will give gifts to Luka and will take "Requests" from Luka.