020: Darts Tournament

Proposed by Toby Walsh

Dart competitions in pubs often have prizes for the first, second, third and fourth best throwers. What is the order of play for a darts tournament involving n throwers that:

1. identifies the best $k$ throwers (and their order);
2. has the least number of matches thrown;
3. has the least number of games on each of $m$ dartboards (since tournaments typically run in parallel);
4. and is the most exciting (that is, prize winners should be discovered at the last possible minute so that everyone stays drinking beer until the end of the tournament).