Yesterday’s fiasco in the Olympic badminton women’s doubles competition provides an unusually vivid illustration of the perils of designing mechanisms that violate incentive constraints. The competition is structured in two stages: a round-robin stage in which the teams compete to earn placement in a second-stage single-elimination tournament. The second-seeded team in the competition, Tian Qing and Zhao Yunlei of China, suffered an upset loss to a Danish team in the first stage. As a result, they were placed as one of the lowest-seeded teams in the second-stage tournament. At that point it became advantageous for the remaining teams that had already secured a second-stage berth to lose their final first-stage match in order to avoid being paired against Qing and Yunlei in the first round of the second stage. Spectators watched in frustration and disbelief as the athletes deliberately served into the net and hit shots out of bounds in an effort to lose the match. Olympic officials afterward decided to disqualify the offending teams from the competition.
There are at least two things that I find striking about this incident. As an algorithmic game theorist (or should I say AGT/E theorist?) I’ve read numerous theory papers containing examples where rational users of non-truthful mechanisms might manipulate it in ways that are shockingly contrary to the mechanism’s intent. Meanwhile, in the real world, people manipulate non-truthful mechanisms all the time but in ways that lack the shock value of the badminton example. (For instance, bidders in a first-price auction shade down their bids a little bit to avoid paying a higher price.) There’s even a growing body of work — for instance, papers such as these — adopting a price-of-anarchy perspective on non-truthful auctions and proving that their equilibria are only moderately inefficient. So what about the aforementioned counterexamples where the outcome of rational behavior is diametrically opposed to the mechanism designer’s intent? The Olympic badminton incident is a welcome example of how these occurrences can happen in real life, not just in the nightmares of theoreticians. Is it time for the International Olympic Committee to start reading research papers on Nonmanipulable Selections from a Tournament?
My other reaction to this news – which stems from my interest in sports, not in game theory – is, “Why doesn’t this happen all the time in sports?” I know of one other example of similarly counterintuitive behavior in sports: the bizarre phenomenon of track sprints in cycling, where racers ride as slowly as possible until the final 200 meters, sometimes coming to a complete standstill, because a racer expends much less effort when “drafting” behind an opponent, creating a disincentive to take the lead.
The bike-racing example is thematically related to what happened in the Olympic badminton tournament, but why don’t we see more occurrences of the exact same type of manipulation as yesterday’s badminton matches? Many sporting tournaments are structured in a way that seems to permit these manipulations. The FIFA World Cup has an initial stage of round-robin tournaments among disjoint groups of teams, with the leading teams in each group advancing to a single-elimination tournament. Have there been cases of teams deliberately losing their final round-robin match to secure a more attractive place in the second-stage tournament? I’m not aware of any such cases, but I’m not well versed in World Cup history. Numerous team sports in the U.S. have a regular season followed by a single-elimination playoff. It’s well known that teams don’t try their hardest after securing a playoff berth (at least in American football where the potential cost of injuring a key player outweighs the potential benefit of improving one’s seeding in the playoff tournament) but that’s different from having an incentive to deliberately lose. The equivalent of the badminton story could easily happen in the NFL: a strong team suffers an anomalous number of losses in the regular season but reaches the playoffs; should opposing teams intentionally lose games to secure a low playoff seeding? I don’t think this has ever happened in the NFL, but why not? One theory is that the ultimate factor motivating teams is profit, not playoff victories, so there is a strong disincentive to engage in behavior that angers the team’s fans. Alternatively the explanation might depend on more superficial aspects of the NFL playoff system, such as the fact that the playoff tree is partitioned into NFC and AFC subtrees irrespective of the relative strengths of the teams, and the fact that the tree doesn’t have constant depth due to wild-card games. Both of these aspects reduce the number of opportunities for an NFL team to perversely benefit in the playoffs by lowering its ranking in the regular season.