Characterizing Potentially Optimal Line-Up Orders in Team Competitions

Team matches for two-person games / sports, e.g. chess are considered. In a competition between two teams A and B each player of team A has to play against exactly one player of team B. To arrange this assignment each team chooses a line-up. For the line-up the playing strength is the most common criterion. The best player of A should be the rst and so on. Assuming that team A has lined up its players according to their strengths, which line-up should team B opt for? We characterize all potentially optimal line-ups for such a team match. It turns out that there are F2n such line-ups for n players, where (F1, F2, F3, F4, F5, . . . ) = (0, 1, 1, 2, 3, . . . ) are the Fibonacci numbers.