This app was mentioned in 12 comments, with an average of 1.42 upvotes
I'm a bit late to this thread but posting for OP's benefit. The Firm! I don't know many people who have played it but more people really should! It's not free but there are no IAPs and it's pretty cheap 84p on android atm.
Basically you're a clerk at a firm buying and selling shares/stocks of companies by swiping left or right to buy or sell. You get promoted for making money and you can get little power ups that you buy (Not IAPs!) with the currency you earn. A really fun, really addictive little game with a lot of replay value and great for a 5 minute blast here and there.
https://play.google.com/store/apps/details?id=ch.sunnysidegames.thefirm&hl=en
My most recent digital purchase was The Firm, for $0.99, last week.
I expected to uninstall it quite quickly. I never stay interested in twitch/reflex games, they're good for an afternoon of entertainment at best - I'm more of a roguelike fan, turn-based methodical play is the sort of thing I look for in a game "for life". BUT, lo and behold, I've been playing The Firm all week and I still love it! So that's definitely a dollar well spent. I recommend it, it's gorgeous.
My most recent physical purchase was a small bunch of bananas for about the same amount of money. I ate the whole thing in one sitting. I may have a problem.
There's a new game coming out this year that may scratch that itch: "Not Tonight"
I'm also looking for games like Papers Please.
I've also got a few personal recommendations:
This is The Police (Strongly recommend - You're the police chief and you manage your station, sending patrols to crime scenes to handle the situations. You need to make choices that affect the outcome of certain situations)
Unsolicited (Broswer free game from the same dev as Papers Please - Lucas Pope - You need to fill paperwork for charities, insurance companies, timeshares, etc)
The Republia Times (Broswer free, also from Lucas Pope - You manage a news paper and need to make choices that affect public opinion)
The Westport Independent (Heavily inspired by Papers Please - You manage a news paper and need to make choices that affect public opinion)
Beat Cop (Really Cool game - You play a cop that patrols a street. You need to keep factions under control, write tickets, speak to people and help them, etc)
Limbs (Browser free game - You need to repair prosthetic limbs)
Beholder (You are the State-installed manager of an apartment building. You'll need to spy on your tenants to make sure that they're following the rules and report on them when they're not. You'll have to make choices.)
For Android and IOS you got 'The Firm'
It might be The Firm.