For the experiment, I have the data on the number of times each particular coalition was formed. It can be visually represented on a bar chart (see the attached image), on which each colored bar corresponds to each of the possible coalitions, and the vertical axis shows the number of times it occurred (count variables).

My general idea is to understand whether stable coalition relationships emerge between participants in the experiment as they play repeatedly: for example, whether participant 1 tends to form coalitions with participant 2 more often than with other players.

To that end, I would like to test:

1. Whether there are statistical differences between the frequency of occurrences of different coalitions;

2. Whether the experimentally observed frequency distribution statistically differs from a theoretical benchmark (each coalition occurs with the equal 1/6=0.15 probability).

What would be the appropriate test in this case given that we are working with count data which is (a) coutn data and not normally distributed, (b) is largely skewed (a numeric outcome is frequently zero)? My guess would be to use Wilcoxon MW test for (1) and Kolmogorov Smirnov test for (2) but I am not sure I can because of the problems (a) and (b) described above and therefore would appreciate any thoughts on this problem...

Thank you very much in advance!