Dear Michael, I've found your demonstration both interesting (because I've learn something) and strange because I think that you've demonstrated nothing about "competition/cooperation". You've based your demonstration on an hierarchical organisation and used its property (multiple levels) to derive a conclusion (or nor conclusion) for the "competition/cooperation". You have showed that both can occur at every level of the organisation. Well this is idiosyncratic with the organisation structure (hierarchy) not with the couple "competition/cooperation". You can apply it to everything, for example "Blue and red office", "eat italian or chineese food". Your demonstration will work. At every level, you will find people "eating pizza"  or "drinking chineese soap" or having an office with blue or green or red. In fact you are projecting "competition/cooperation" on a structure but your mapping is not an isomorphism so you should not conclude anything about "cooperation/competition". "Cooperation/Competition", both  also occur outside the frame of organisation. Theses nominalisations are processes and trying to fit then into an hierarchy do not seem to lead somewhere. We can described them only IN RELATION TO A GOAL". So the right question might be "Are they at the same logical type" ? If your goal, with a group of N guys is to have them producting more stuff then both "competition/cooperation" can be of help so it might be said that they are of the same logical type. Now, having N guys "working one by one" (something close to competition) or "trying to combine their effort and competence"  (something like cooperation) seem to be of a different logical TYPE. It depends of your definition of "competition" and "cooperation". As you rightly outline, even in competitive contexts like sales, there is both "cooperation and competition". That also true for the Superboal, you need two finalists to make a final so they are both cooperating and competiting. All the Best JPG