The Quantitative Peace

The Military and Competitive Sports

I missed my last post, but thankfully I'm on top of this week's edition. 

Kyleanne Hunter and Oliver Kaplan have a piece at Political Violence @ a Glance discussing some of the military roots of the biathlon. I've never known much about the sport's history, but it certainly makes sense that its origins are so closely tied to the kinds of security needs that Hunter and Kaplan cite. This was particularly interesting to me as both my wife and I grew up close to Lake Placid, New York. Lake Placid hosted the winter Olympics twice—once in 1932 and again in 1980—and continues to be a destination for tourists and athletes alike. Additionally, the 10th Mountain Division is headquartered about three hours from there at Fort Drum, and they have an armory located in Saranac Lake, New York where I grew up. Two members of the US biathlon team are also from Saranac Lake: Annelies Cook and Tim Burke. 

I went to high school with both Annelies and Tim, and it's great to see them doing so well. Hunter and Kaplan's discussion of the biathlon's history also makes me appreciate the sport and where I grew up a little bit more, and it's neat to think about the sport in terms of how it intersects with my own personal historical/research interests. The idea that specific military assignments can evolve into cooperative/competitive sporting events is really interesting, and I'm sure there's been much more written about it than I'm aware of (which is little). Naturally this makes me wonder what other sports have evolved out of military activities. Archery comes to mind, but I suspect that has competitive origins that are less exclusively military. There are a number of other shooting-related events during the summer games (see here), but again, many of these events are not necessarily exclusively military in origin either. Some of the historical information the link provides, and the descriptions of some of the events, suggest more of a hunting-related background. And many of these events appear to have been phased out, or have only been held once or twice.

It also makes me wonder as to what kind of selection effects might be at work in terms of how these activities evolve into competitive sports. Presumably you need activities that are a mixture of some highly specialized skill, but also something that's not overly secretive. After all, you don't want other states knowing that you have individuals highly trained in a particular task if that will compromise their work in some way. You also need an activity where multiple countries have need of the same type of training or force. As Hunter and Kaplan discuss, multiple countries were deploying similar sorts of forces to patrol remote, mountainous border regions, thereby facilitating the development of some sort of competitive event based on these shared activities. So not every state needs to have a given force, but at least a few do in order for it to be competitive. 

So what are some contemporary examples of the sorts of military activities that could evolve into internationally competitive sports? And how has technological innovation changed the landscape, so to speak, in terms of the pool of potential activities that could evolve in this way? My mind immediately went to some underwater sports, thinking of some combination of navigating an underwater obstacle course, and then performing some task requiring a demonstration of dexterity. This list of underwater sports suggests there are some sports that at least partly resemble these activities. Underwater navigation and underwater target shooting, specifically. This article also indicates that no underwater sports have been a part of the Olympic games. This appears to be due to the International Olympic Committee selecting which games it will grant approval to. Still, these seem like activities that require a high degree of specialization, but are also pursued by enough countries to facilitate competition. 

Another future possibility would be sort sort of aerial drone competition. Competitors might be judged on their ability to take off, perform certain maneuvers, perhaps "paint" a moving target for a given period of time, and then land. Though there are more advanced military variants, less sophisticated and less expensive drone variants are already being experimented with for a variety of purposes (see Amazon's recent talk of drone-based delivery). Though this would certainly emphasize physical performance less than other athletic activities, I'm not sure it's all that different from other activities like shooting, much of which emphasizes hand-eye coordination. This is also technology that more countries are likely to pursue for security/military purposes as time goes on.

If anyone can think of other military activities that might translate into internationally competitive sports, please share in the comments. 

When losing is the winning strategy: Game Theory, Badminton, and the 2012 Summer Olympics

The Badminton World Federation disqualified four female badminton teams today from the London Olympics for unsportsmanlike behavior. These teams purposefully tried to lose their first match in a round robin event in order to be paired against easier teams in subsequent rounds (video recap here). These teams were obviously cheating as purposely losing in this manner is against the badminton rules. So why would so many teams blatantly cheat in a very public and very important sporting event? Because they thought they could get away with it. Prior to this mass banning of teams, several Chinese teams had a history of purposefully trying to lose in badminton matches and they were never punished for their behavior.

Being able to cheat and get away with it gave the Chinese teams a huge advantage in the Olympics. Hence, other teams followed the example of the Chinese teams and tried to lose, so they would also have an advantage in later rounds of the competition. All the cheating teams believed there existed a low probability of being caught and/or punished for cheating given past examples.

I created a game to demonstrate why it was in the best interest of all the badminton teams to try to lose their first badminton matches, assuming there was a very low probability that they would be caught.

The Players

There are two players in this game, Team 1 and Team 2. Team 1 is the better team. They have a 60% chance of winning the match if both teams play fairly. Team 2 is the weaker team. They only have a 40% chance of winning the match if both teams play fairly.

Both teams want to lose the match (while the A team is the better team in this particular round, they would rather have easier competition in subsequent rounds of tournament play). If a team loses, they receive 10 points. Alternatively, if a team wins, they receive 0 points.

Nature also plays a role in this game. Nature represents both the probability that the team will be found cheating and punished for their behavior.  If Nature decides that a team played unfairly, Nature will punish the team, but only 5% of the time.  Given that punishment has been rare in the past, this probability is reasonable, but can be altered to change the risk/reward ratio for cheating. If a team is caught cheating, they receive -10 points.

The Moves (See Figure 1)

Team 1 goes first. They can “Cooperate” and try to win the game, or they can “Defect”, and purposefully try to lose.

Team 2 moves next. They observed Team 1’s move. Team 2 can also “Cooperate” and try to win the game, or “Defect”, and purposefully try to lose.

The Outcomes

There are four outcomes.

1. Both teams Cooperate

For this outcome, both teams played fairly and tried to win the game. Team 1 wins 60% of the time when this occurs, and Team 2 wins 40% of the time. A team receives 0 points for winning and 10 points for losing. Hence, the expected utility for each team if this outcome occurs is:

([(0.6*0)+(0.4*10)] , [(0.4*0)+(0.6*10)]) = (4, 6)

2. Team 1 Cooperates, Team 2 Defects

For this outcome, Team 1 tried to win and Team 2 tried to lose. Team 1 wins with a 100% probability and receives 0 points for winning.

Since Team 2 cheated, there is a probability that Nature will punish them. Nature punishes Team 2 5% of the time. If Team 2 is punished, they receive -10 points. The other 95% of the time, Team 2 gets away with it and receives 10 points for losing.

The expected utility for each team if this outcome occurs is:

(0, [(0.95*10)+(0.05*-10)]) = (0, 9)

3. Team 1 Defects, Team 2 Cooperates

For this outcome, Team 1 tried to lose and Team 2 tried to win. Team 2 wins with a 100% probability and receives 0 points for winning.

Since Team 1 cheated, there is a probability that Nature will punish them. Nature punishes Team 1 5% of the time. If Team 1 is punished, they receive -10 points. The other 95% of the time, Team 1 gets away with it and receives 10 points for losing.

The expected utility for each team if this outcome occurs is:

([(0.95*10)+(0.05*-10)], 0) = (9, 0)

4. Team 1 Defects, Team 2 Defects

For this outcome, both teams tried to lose. Since both teams tried to lose, there is a 50% chance that any team could win.

If a team wins, and Nature does not catch them cheating (which happens 95% of the time), the team receives 0 points.

If a team loses, and Nature does not catch them cheating (which happens 95% of the time), the team receives 10 points.

If Nature catches a team cheating (which happens 5% of the time), regardless of whether the team won or lost, the team receives -10 points.

The expected utility for each team if this outcome occurs is:

([(0.5*(0.95*0))+(0.5*(0.95*10))+(0.05*-10)], [(0.5*(0.95*0))+(0.5*(0.95*10))+(0.05*-10)]) = (4.25, 4.25)

The Nash Equilibria (See Figures 2 and 3)

There is one Nash Equilibrium derived from backwards induction, {Defect; Defect, Defect}.

There are two Nash Equilibria derived from the strategic form game, {Defect; Cooperate, Defect} and {Defect; Defect, Defect}.

This game suggests that as long as the Badminton World Federation rarely punishes players for trying to lose in the first match of a round robin even, it is in a team’s best interest to try to cheat early on in order to improve their chances of winning in subsequent rounds. To change this outcome, the Badminton World Federation should either detect and punish cheating more often, or change the rules of the tournament where losing in an early round is not so advantageous.

(For another interesting sports match- the 1994 Caribbean Cup provides a classic example of how rules fundamentally change the expected behavior of players in an environment where the object of the game appears simple. By the end of the game, it was in the best interest of both teams to try to score points for the other team).