Atzil et al. (2018):
I felt it's unclear what sociality or being social means here and in general. Is it the ability to engage in social interactions? Is it the motivation to engage in social interactions? The ability seems easier to characterize, because the motivations (and demotivations) seem rather diverse (being around other minds feels good, seeking validation, it provides a distraction from one's internal dark thoughts, you are looking for a life partner or friends or other activity-partners, vs probably more). However, the paper seems to lean towards the later; but it also makes a distinction between allostasis and homeostasis. I'm unable to follow why the predictions of allostasis are the way they are; the connections seem vague.
It also seems to put a large emphasis on social experience as infants; but it seems close friends and partners (and even books and other media!), atleast during adolescence and early adulthood, can have a big impact on how and why we yearn or do not yearn to spend time with others.
Lockwood et al. (2020):
At the outset, I felt this would turn out nice. But it seems to reduce the computational goals to cooperation, affiliation, or competition; the word 'affiliation' never seems mentioned again. I think it's still a reasonable attempt at delineating processes that happen in social vs nonsocial contexts.
About rewards, I suspect that outside of simple-laboratory experiments, it'd be more fruitful to rely on Level-K framework or Adam Mortan's "Solution Thinking" (reference to Francesco Guala's colloquium) to rely on for explanation or modeling. For instance, suppose a friend asks me to do their homework. The immediate argument might be that if I am competitive, I should not do their homework; and if I am cooperative, I should do their homework. However, I might reason that doing the homework is beneficial because it helps one in the long run. So, I might do it because I want them to remain dumb (competitive), or I might refuse to do because I want them to struggle and learn (cooperative). And one can add further layers.