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That's exactly what I had in mind. For example, BK from our side and Pit from your side could lead the negotiations.
But at the same time, they can (and probably should) consult with the most trusted members of their teams.
In general, if the idea of holding a tournament catches the attention of at least 3-4 top players from each side in the near future, then it's a matter of organization and team building. And let the battle begin!:p
The main idea of the tournament (and its novelty): each top player will have the right to make a mistake, and each newbie will have a chance to influence the outcome of the match. It will be like in professional team sports!;)
...Messi outplays half the team, shoots at an empty net... the post!.. but the ball bounces off the knee of an awkward 17-year-old rookie who came on as a substitute... and a goal! and Barcelona still wins!;)