Last night I finished Papers, Please. I'm about five years late to the party, but the upside of being so late is that it's perhaps a fresh game to bring up again. Here's what I like:
Papers, Please is an excellent example of how to apply scarcity into game design.
First - the lore works perfectly to highlight and explain the various scarcities within the game. An oppressive government for a country with diminishing resources and tight social control make the various scarcities simultaneously believable and engaging. You might not be able to get away with making resources so tight, unless you explain it with lore, and this game does it with apparent effortlessness.
Anyway, the most profound scarcity in this game is time. Your family's livelihood depends on your ability to do stuff quickly - and later on, so does the health of people like Sergio (or yourself). Your pay depends on how many people you can quickly (and properly) check, and so the time restriction gives you a sense of urgency. The otherwise menial task of correlating documents suddenly gets your heart pumping a bit.
The scarcity of time only works because other variables stem from it. For example, because players don't make much money per day, the average player can't pay for both food and heat consistently. Players always feel the strain of forcing their family to endure one type of sadness or another. The lore of making your family suffer + the mechanics of losing the game if you go broke turn cash into a premium resource. Therefore, the scarcity of money motivates players to work as quickly as they can and optimize their reading skills. Your money troubles also motivates you to take bribes, which is useful for introducing quandaries. Linking variables like this gives a kind of distance from the time variable. Technically, what you mostly need is money, not specifically time. Instead, you kind of force yourself to optimize time on your own as the 'solution' to money problems. I think when the player puts importance on time on their own, it really helps them get invested in the game.
There's even scarcity of desk space, especially later on in the game, that makes work feel even more stressful. (It also rewards planning ahead and good spacial management, so players who are slow readers or poor at memorization can make up for it with a good system for document arrangement.)
Now that I've laid some groundwork, my point is this: Papers, Please took a very, VERY boring task and made it mechanically interesting just through a mix of number tweaks and story concepts. Careful tuning made it so you wish you had just one more minute, or just ten more credits. Rather than making the gameplay tasks intrinsically appealing, Lucas Pope limited your ability to do them properly. And before you know it, this game's masterful application of scarcity has you stressing out about people's heights and birthdays.