Here’s what game theory says about how to win in semifinals

When it comes to tournament-style competitions, people tend to focus on the championship round: the Super Bowl, the general election, the final interviews for a job opening. But consider the importance of the semifinal. A loss guarantees a finish of no better than third place, but the all-out effort needed for winning can bring a high cost: Competitors may be too drained in the championship.

Exploring this semifinalists’ dilemma, physicist Hyeong-Chai Jeong at Sejong University in Seoul, South Korea, and colleagues used game theory to determine optimal strategies for four evenly matched semifinalists. In a winner-takes-all format, Jeong’s team says it’s best to match opponents’ strategies, such as resting key players. That way, rival semifinalists can stay competitive with each other and have enough left in the tank for a potential final.

Competitors have more options if they’re willing to settle for bronze. They can exert maximum effort in the semifinal and, if they win, accept a likely loss in the final. Or they can coast in the semifinal, expecting to lose, and go all-out in the third-place match.

The analysis, published in the April Physical Review E, could offer lessons for competitors and those who organize other types of competitions. For the business world, Jeong advises companies to offer several plum leadership positions so that employees aim to diversify their skills rather than converge on a similar strategy to land a single coveted post.