The hypothetical Communist citizen's incentive is...
Having a nicer life. By furthering the common interest, we can further our own self interests.
Also, note: I do support some scaling in terms of payment: more difficult and more unpleasant jobs should have greater rewards. I just want those rewards to actually reflect on how difficult and unpleasant a job is, and I want the scaling to be relatively gentle.
Okay, but that doesn't work in reality, and besides the calculation problem (which I already went over), the problem with incentives is another nail in the Communist coffin.
Imagine you work on a collective farm with 99 other workers picking potatoes. Of these potato pickers, let's assume that each picks an average of 10 bags of potatoes a day for a total of 1000 potato bags, of which some are given to those who make other products and the rest are left for eating. So each worker receives the equivalent value of 10 bags of potatoes each day. So imagine that one day, in a fit of "self interest", you decide to work to become a great potato picker, and manage to increase your picking rate to 12 bags each day, or a 20% increase. Despite increasing your picking speed by 20%, the total pool of potatoes has only increased to 1002, and you now receive the value of... 10.02 bags of potatoes each day. Now imagine you become a god of potato pickers and increase your speed to 30 bags each day. Despite having increased your speed by a colossal 300%, you only receive 10.3 bags each day, meaning you still haven't functionally improved your position. Inversely, if you slack off and only pick 1 bag each day, you receive 9.91 bags each day, despite contributing next to nothing. Unless potato picking fills you with joy, the "optimal" thing for you to do every day is to slack off and let everyone else increase picking on your behalf since your contribution is very nearly irrelevant regardless of how hard working or lazy your coworkers are.
That's an odd example, seeing as most capitalist versions of that institution don't scale pay at all based on how much work you do. If you do enough to avoid getting fired, you get your minimum wage, if you don't, then you get the axe. If I were organizing that potato farm according to my communist ideals, I'd probably have payment be based on how difficult & undesirable the job is, with slight adjustments based on how productive you were. If you were unproductive enough, the rest of the group might vote to dismiss you, leaving you to find another job or get welfare. And of course, most of the incentive would probably come from your coworkers calling you lazy.
On a societal level, I'd want to put a lot of resources towards things like medical research and therapy, so that people who aren't able to
work for some reason or another can be treated so they can. And of course, I'd definitely automate potato picking.
Note, my communist ideals vary fairly significantly from the more mainstream ones. I want a decentralized communist economy, and a very thoroughly democratic government.