Tournaments with subsequent group stages are incentive incompatible

We discuss the strategy-proofness of multistage tournaments. In a tournament with subsequent group stages, players are divided into groups in the preliminary and main rounds, where they play pairwise matches against each other. The higher ranked players qualify to the next stage such that matches are not repeated in the main round if two qualified players have already faced in the preliminary round. Players prefer to carry over better results to the main round, provided that they qualify. It is shown that these tournament systems, widely used in handball, are incentive incompatible. We also present some historical examples where a team was ex ante not interested in winning by a high margin