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.
There is an interesting discussion of possible solutions in the comments to this post: http://cheaptalk.org/2012/08/01/lets-write-this-paper/
http://en.wikipedia.org/wiki/Barbados_v_Grenada_(1994)
“However, the Barbados players started defending their opposition’s goal to prevent them from doing this, and during the game’s last five minutes, the fans were treated to the incredible sight of Grenada trying to score in either goal. Barbados also defended both ends of the pitch, and held off Grenada for the final five minutes, sending the game into extra time. In extra time, Barbados notched the game-winner, and, according to the rules, was awarded a 4-2 victory, which put them through to the next round.
”
Video here : http://www.youtube.com/watch?feature=player_embedded&v=ThpYsN-4p7w
Actually tanking is not uncommon in American professional sports, where the last placed team usually gets first pick in the lottery (like the NFL). The incentives for this exist, although I doubt any team is willing to admit to it. In the NBA, the bottom teams end up in a lottery for the first pick, where the worst team only has the highest probability of getting the first pick (so a randomized mechanism !). Even there, teams tank a little, but the randomization makes it less reliable. In baseball this doesn’t happen as much because the draft isn’t the most impactful way of improving team quality.
Another way teams tank in the NBA is by gutting their payroll (and losing big time) and taking losses now to prepare themselves for a coveted free agent later (see James, LeBron and Howard, Dwight :)).
Pre-playoff tanking to avoid injury happens less because of the mental aspects of “a habit of winning”.
Here’s a famous example of collusion:
http://www.guardian.co.uk/football/2010/jun/13/1982-world-cup-algeria
Here’s a mechanism based on Suresh’s comment. Given a subset of teams that progress to the second round, we choose the tournament bracket uniformly at random. To incentivize teams to do as well as possible in the first round, we let the probability of advancing to the second round increase with the team’s score.
Actually, this reminds me that someone (Vince, was it you?) told me that in his country (the Netherlands, if it was Vince) there is a national lottery for places at medical schools, and your probability of being accepted increases with your grades.
This makes me think that the real mistake was made by the players, in making their tactic so obvious. There’s a fair bit of subtle playoff positioning in the NBA or so it seems, but there’s no way to detect it if done carefully.
If these players had been more subtle, the complexity of executing such a strategy may have introduced more failure, and therefore less gamesmanship. I wonder if there’s a way to model that 🙂
This is also related to the reason of why the last match of the first stage is played at the same time, for all the competitors. This happens in football at Champions League, Euro Cup, World Cup and even Olympics.
Another interesting example for studying strategy proof behavior occured at the last Football Euro Cup. In some cases, it is strategy proof to arrange a tie and eliminate consequently a strong opponent – the case of the last match of the group stage between Spain and Croatia, where if they both tied 2-2, then Italy will be eliminated-. Arranging a tie seemed to be an strategy proof behavior-Croatia will go to the last round, and Spain will be first in his group, and aditionally eliminating such a strong competitor as Italy. Anyway, Spain played well and defeated Croatia -an irrational desicion?- and at the end of the tournament they played the final against…Italy! Well, In the end Spain won the tournament anyway.
Game Theory is everywhere!
In soccer World Cup and Champions League they get around the trap by pairing the leaders of each group with the runner-ups of the other groups, so there’s always the incentive to become leader, in order to face easier teams on the elimination stage and last longer in the competition
They do the same thing in olympic badminton; however, as Bobby mentioned, the upset loss in one group cause the leader to be the second best team and the runner up to be the best team.
@Alex, they tried something similar here also, just that the seeding went wrong in this particular case.
Some more examples I can think of
– Suarez’s hand ball in the world cup http://en.wikipedia.org/wiki/2010_FIFA_World_Cup_knockout_stage#Uruguay_vs_Ghana
– Intentionally losing points in a set which you are sure of losing, so that you can play better in the next set.
It also brings up an interesting question – are the players responsible for putting up their best performance throughout the tournament, or should they adopt such tactical measures to increase their success chances? I think the players should be free to do what they like. How is it different from a long distance runner not running at his full speed in the beginning of the race?
I remember the Uruguay-Ghana match! It was amazing, but a slightly different case. The defender prevented a clear goal at the cost of a penalty kick, which is less than 100% probability of a goal (and indeed the penalty kick was wasted and Uruguay won in the end). You could say the defender sacrificed his own standing for the team, but at team level it was a clearly rational behavior, trying to win the game.
The thing that I find most annoying about this incident is that in sports it should be completely understood that teams will strategize on the whole tournament not just individual rounds. The terms of the tournament were set by the olympic officials (or precedent). The players shouldn’t be disqualified; olympic officials should be fired.
In the NFL this past season several teams (Dolphins, Colts, Rams) were encouraged by their fans to “suck for luck”, i.e. to rank lowest among the NFL teams in order to get the first draft pick and select Stanford QB Andrew Luck.
This has actually resulted in talks of instituting some sort of weighted lottery for draft pick placement.
I forgot another classic example, in Euro 2004 group C, in the last round Sweden was playing Denmark, where it was known that if the match ended in a 2-2 (or more) draw both would qualify, eliminating Italy. A lower scoring draw (as well as any team beating the other one) would have the potential to allow Italy to qualify for the next stage instead of one the Scandinavians. The match did end in 2-2, and though some allegations of colluding were made, nothing came out of it.
In the 1982 football World Cup, England and France were in the same group. England beat France and went on to top the group, with France coming second. There was then a second group stage with three teams per group. As a result of coming top, England got into a group of three with West Germany and Spain, from which one team qualified, which was West Germany (as will be no surprise to anyone who has followed English football). France got into a much easier group, with Austria and Northern Ireland, which they won and as a result reached the semifinal. It’s not quite an example of perverse incentives, because it probably wasn’t obvious when England played France that it was a match that they wanted to lose, but it is certainly an example of a perverse outcome. No, I’m not bitter … honest.
As a sports fan, particularly a football fan we do see this happen often. I remember in 1991 when the Skins went 14-2. After they had guaranteed the top spot in the playoffs. After that point there was no real incentive for them to “compete” other than playing for pride. This happens every year in the NFL when teams lock up that first seed early. I remember the Colts question was generally whether or not to rest Manning for the playoffs. The Patriots in their 18-1 season played that last game in the regular season against the Giants with no real incentive for winning as they were guaranteed the number one spot. It even happened in the NBA last year when the Wizards went on their 6 game late season winning streak because they were playing playoff teams who were already locked into their spots and thus had no real incentive for winning a meaningless game and thought it more beneficial to rest their starters for the playoffs.
Its a pretty common thing, although not generally as obvious as it was at the Olympics (and not generally on such a large scale either). The NFL tried to plan against this by making the late season games more important by putting things like more division and conference games late, but that still didn’t stop GB from starting off the season undefeated and locking up that top seed early.
But the NFL argument is that its hard to turn “it” off and on like these players were trying to do. Playing to lose is a different mindset and can lead to players not giving their all on each play, which makes injuries more likely and that can really hurt a team’s playoff chances. Even without injuries though, trying to turn “it” back on after turning “it” off is a hard thing that’s much more complicated than flipping a switch and unless you’ve got a team like the 49ers or the Skins of the 80s or the Bulls of the 90s, then its just not something that’s likely to be beneficial.
Counting cards can turn blackjack into a (slightly) winning game for the player. However, casinos are permitted to refuse service to anyone, and typically do so if they believe somebody is counting cards and doing well. This leads to a situation where a good card counter sometimes has to make stupid plays to disguise the fact that they are counting cards.
I would just like to mention that the cycling example does not fit into this discussion. Standing still and forcing the other to take the lead is part of the tactics and actually makes this discipline the most exiting in indoor cycling (in my opinion). At the end it only counts who is first. Since most of these tournaments are done with a knockout system, nobody has the incentive to lose.
I actually wanted to write a blog post on it after getting out of camp from reservist military training. Then I found this wonderful article. =)
On the matter of why it doesn’t happen more, I’d say that “side payments” such as ad revenue provide subsidiary incentives to exhibit some “honor on the field”. Which is probably why top teams are incentivised to be at the top of their game almost all the time. Picture perfect sporting moments bring in ad money. So its all about payments.
In sports like badminton, these payments are not substantial enough to detract from strategic skiving.
Similar things happen quite frequently in cricket.
For instance, in the 1999 world cup, the Australians deliberately batted slowly against the West-Indies so that West-Indies could qualify for the super-six stage of the tournament ahead of New Zealand based on net run-rate, which would mean that the Australia would carry over points into the super-six stage. (Australia beat West-Indies but lost to the Kiwis. Eventually though the Kiwis qualified by battering Scotland and thereby increasing their net run-rate.) http://www.independent.co.uk/sport/cricket-world-cup-australian-goslow-angers-fans-1096980.html
Another instance is when Sri Lanka deliberately lost to India in a preliminary game of the Asia cup 2008 so that they could face India ahead of Pakistan in the finals. (For some reason, Sri Lanka felt that India is easier to handle in the finals, than Pakistan.)
http://www.indianexpress.com/news/former-stars-claim-sl-lost-deliberately/331559/
There have also been occasions where players have been deliberately rested so that the opposition face them only at a later stage in the tournament. One incident that comes to my mind is the super-eight match involving Sri Lanka and Australia in the 2007 world cup, where the Sri Lankans rested Vaas and Muralitharan so that the Australian batsman do not get used to their bowling. Also, Sri Lanka did not mind losing that match since if losing the match will enable them playing their semifinal at a more favorable venue.
http://www.smh.com.au/news/cricket/sri-lanka-tactics-a-disgrace/2007/04/17/1176696836755.html
There have been plenty of other such instance in cricket but these were the three that came to my mind immediately.
Another one in cycling – if things are not going your way, crash and get a restart!
http://www.cnbc.com/id/48479643
BTW in ice hockey championships, the system was changed recently to seed teams from each group against each other (A1-A4, A2-A3, B1-B4, B2-B3), rather than across the two groups (A1-B4, A2-B3, A3-B2, A4-B1). I wonder if it has anything to do with possible manipulation – I think the new system still allows some (e.g. A3-A4 playing the last game when A1 is not the strongest team), but perhaps it’s less likely.
Here is a more subtle example from bridge. Due to the large number of teams in the tournament, the Swiss Team matches used to be a very popular mechanism for the preliminary round. This is essentially a partial round robin where each round the teams are matched up to opponents of similar strength according to their current standing. It is a well known strategy for some teams to deliberately lose the first few matches to get a weaker set of opponents in the long run. And it sometimes works quite well!