There was recently a scandal in the Olympics where some badminton teams were intentionally trying to lose. Now with certain tournament designs, such as the one they used in the Olympics, and also "Swiss system" chess tournaments, it is possible for situations to arise, where intentionally losing your game, increases your expected amount of prize-rewards. But other tournament designs are immune from this problem. For example, in the usual "single elimination" binary-tree design, with winner-takes-all prize-rewards, the unique best strategy is to win every game. In a "round robin" (all-play-all) tourney, where prize money is an increasing function of your total number of wins, again a best strategy is to try to win in each game, but with the asterisks that if you manage to get an insurmountable lead then you can quit trying, and if we were playing chess where "draw" results also are possible, then there would be other issues. Trouble is, binary tree on N players has N-1 edges (games) which is often too few; and round robin on N players has (N-1)*N/2 games, which is often too many. PROBLEM: devise other schemes... One example would be a "tree of round-robins" where the players are partitioned into disjoint subsets, each subset plays a round robin, then the top-K from each subset enter a "round robin of champions" round. I think even better would be to devise a quantitative system for measuring how good any given tournament design is, for example probability it finds the strongest player as "winner" in some probabilistic model of players. Then computation could find the "best" tournament design for N players for each small N. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)