Mitigating the risk of tanking in multi-stage tournaments

Multi-stage tournaments consisting of a round-robin group stage followed by a knockout phase are ubiquitous in sports. However, this format is incentive incompatible if at least two teams from a group advance to the knockout stage where the brackets are predetermined. A model is developed to quantify the risk of tanking in these contests. Our approach is applied to the 2022 FIFA World Cup in order to uncover how its design could have been improved by changing the group labelling policy (a reform that has received no attention before) and the schedule of group matches. The proposed interventions can halve the level of unfairness without changing any fundamental aspect of the tournament.