Endowment effect
Also said as Ownership bias, Mine is better
People value a thing more once they own it. Kahneman, Knetsch and Thaler's 1990 study gave students mugs, and owners asked about twice what others would pay for the same mug.
It tells you that a player will care more about a thing they feel is theirs. It also has limits: Plott and Zeiler showed in 2005 that with careful procedures the gap can shrink or disappear, so how general it is, and why it happens, stays debated.
Say it
“Let players name their first ship and paint it before the first mission, with no stats changing. Then when it gets damaged, they will care about repairing it.”
Where you’ve seen it
XCOM lets you name your soldiers and change how they look. Losing Sergeant Dave, whom you named after your brother, hurts far more than losing a unit.
Not to be confused with sunk cost fallacy
Sunk cost is about what you have paid. The endowment effect can happen with something you were given a minute ago for free.