I am planning a study in which there will be binary repeated outcomes.

In short, participants will interact in groups of three in a group task. Each person in the group has a different role. They will play this group task for a total of 12 rounds. There are three conditions that are played for four rounds each. The experiment will be conducted with sessions of 9 persons, that will be randomly assigned a group composition each round. Each person plays as the same role in all rounds. I am interested in determining the difference in behavior between these three within-subjects conditions for one specific role.

I am now looking to determine the sample size for this study using a small to medium effect size. Should I look at a number of groups or solely the number of participants assigned the role I am interested in? Which software would be best suited to conduct this analysis?

Complicating things more, I would also be interested in testing the effect of an individuals social value orientation (which could be used either binary or continuous).