There are no Perversity Points in Paranoia 2017. However, there are two new things: Number One Troubleshooter and XP Points.
The Number One Troubleshooter is a card—best displayed in a little plastic stand—that can be awarded to the Troubleshooter who best acts in accordance with The Computer's wishes. As soon as another Troubleshooter does something cool, though, you're supposed to immediately move the title to them.
Mechanically, it does nothing. Fictionally, though, other citizens might notice and treat the character in a special way. It's something for the Troubleshooters to compete for.
In the new Paranoia, Alpha Complex is entirely gamified. XP Points can be awarded at The Computer's whim, but the easiest way for the Troubleshooters to earn XP Points is through Achievements, which are provided along with the mission. The mission itself also has a juicy XP Points reward, but this is often reduced based on any mishaps that might occur during the mission. Troubleshooters can spend XP Points anytime to get useful rewards from The Computer, such as weapons, armor, drugs, and improved stats.
To some extent, you can also reward clever players with Equipment cards.