I have data from 20 groups of 5 people (assigned randomly) making binary decisions within the same group for 20 times. Each period, within each group of 5 people, each person chooses A or B depending on what they think the other 4 people are choosing. Now I want to regress choice on outcomes in last period (and history, time) and demographic variables...

My problem: in terms of clustering standard errors, I should be at least looking at the individuals (like in panel data). But should I do anything about the groups (which stay the same across time)? If so, what should I do? cuz each 5 players' decisions obviously depend on each other.

Also, I assume that random effect probit is a good model for the data?

Any help would be much appreciated.