Minimising the risk of tanking in tournaments with a preliminary round-robin group stage

Multi-stage tournaments consisting of a round-robin group stage followed by a knockout phase are ubiquitous in sports. However, as has been verified recently, this format is incentive incompatible if at least two teams from a group advance to the knockout stage where the brackets are predetermined. A framework is proposed to quantify the risk of tanking in these types of tournaments. Our model is applied to the 2022 FIFA World Cup in order to uncover how its design could have been improved by changing the set of groups to be finished before their pairs, a component that has received no attention in the previous literature. Using the suggested approach, tournament organisers are able to compare all feasible schedules at the time of the draw and choose an optimal sequence of matches with respect to avoiding tanking.