The other teams could make trouble for us if they win — Yogi Berra
Another frightening game to consider is called the Tragedy of the Commons. This game can have any number of players. The players share a communal resource which is free for all to use, but if too many people use too much too often, it will be destroyed.
In our example the players are all nations using the planet’s oil reserves*.
* Traditionally, it’s presented as farmers sharing a common pasture for their cows. If used by everyone the pasture will be turned to mud by overgrazing. But really the game applies to any limited or unstable communal resource, and so it seems more topical and personal in today’s society to use oil rather than cows. Moo.
In the World Oil Game, if you use only a reasonable portion of the oil, you will be able to fuel your nation’s industry within reason, but the oil will not be used up so quickly that you don’t have time to develop other technologies and infrastructure in preparation for the inevitable day when the oil is gone.
On the other hand, if you do use as much as you can, you’ll develop your nation faster and better than the nations that are more conservative, leaving them in relative poverty and so making you the de facto world superpower. You’ll still get to convert to another energy source over time as long as everyone else is careful. But if everyone behaves selfishly, you will have collectively left the entire world in a situation where there is quickly no oil left to use, and no technology or infrastructure ready to take its place.
Civilization will collapse*.
* Yes, of course, you can argue that you would smarten up and pull back in time, and technology would save you. But would you? Would all nations? That is, after all, the point of viewing the situation as a game. Would you really at any time let that other nation keep using oil at a frantic pace while you are more frugal and restrained?
A payoff matrix for more than two players can’t be presented easily in two dimensions, but we’ll make due with the following abbreviated form which divides the players into two groups, “fair nations” (those that take only what is advisable) and “greedy nations” (those that selfishly use all of the oil they can).
|Number of Greedy Nations|
|Result||No Greedy Nations||One Greedy Nation||Two Greedy Nations||All Greedy Nations|
|One Round||1, NA||1, 5||1, 5||NA,5|
|End Game||1, NA||1,1||1, 1||-∞, -∞|
Here, the number on the left represents the payoff for any nation that plays fair, while the number on the right represents the payoff any nation that is greedy. The results vary depending on whether its just one round in the middle of the game when oil is plentiful, or at the end of the game when oil is scarce. The results also vary depending on how many nations adopt each strategy.
For one round of the game, the strategy is obvious… be greedy. In the short term, your nation will benefit and no one will suffer, no matter what they choose to do. A country that is fair in its use of oil resources will be comparatively poor, but that’s their problem.
By the end of the game, defined as some tipping point where resources are dangerously close to running out, a single greedy nation or two will no longer have the option to be greedy, but they are also no worse off than the nations that had been fair in their resource usage. In fact, by now they’ve accumulated a lot more points (wealth) and by so doing are perhaps slightly better positioned (if they were wise and thought ahead) to deal with the impending oil crash.
Unless, of course, everyone is greedy (or too many nations are greedy) throughout the game. In this case, the oil is used up too quickly, the nations’ economies do not have time to revise their infrastructure, and civilization collapses. All nations, regardless of how they played the game previously, are far worse off no matter how well they did in previous rounds and how much wealth they had accumulated.
It all vanishes in the Tragedy of the Commons.
If the world were perfect, it wouldn’t be. — Yogi Berra
If you walk through a very old graveyard in New England, you are likely to notice something about the tombstones in the cemetery that differs from more modern cemetaries. There are a lot more people that died a lot younger.
In today’s society, we take security and long life almost for granted. Clean drinking water plays a huge part in that, as does good medical care, better rules and regulations for safety, well organized, trained and equipped fire and police departments, and other factors. We live much longer, are much healthier and live more safely than did people three or five hundred years ago.
We also have vaccines, which have helped to wipe out once virulent scourges like small pox and polio. Cars are equipped with powerful, computer designed and crash tested frames, and seat belts, and air bags.
But we take our gluttonous hunger for security even further than mere health. We don’t want to risk physical loss, but we also don’t want to risk monetary loss, so we have insurance. We have car insurance, health insurance, and home owner’s insurance. Businesses carry liability insurance. Some people carry disability insurance, and life insurance for a spouse.
By paying taxes to the government, we also have unemployment insurance, and “retirement insurance” (social security, pensions and retirement plans). Most countries have “invasion insurance” in the form of an organized, trained and expensively equipped army, air force and navy.
We are all extremely risk averse individuals living in a risk averse society.
The Vaccination Game
If you don’t set goals, you can’t regret not reaching them. — Yogi Berra
Some games aren’t clear cut. Using game theory to evaluate whether or not to get vaccinated, or to vaccinate a child, doesn’t help. Generally, if you get the vaccine, you won’t get the disease, likely a serious one, but there also might be serious side effects. In both cases, it’s hard to pin probabilities on either outcome. The penalties for a mistake may be serious, but the likelihood of some outcomes is so small as to be difficult to compare.
The payoff matrix looks like this:
|What Happens||Get Vaccinated||No Vaccination|
|Exposed to Disease||0||-∞|
|Suffer Side Effects||-∞||0|
Here, it’s assumed that either bad result, either getting the disease or suffering the side effects, is a very, very bad, life changing event.
There’s no clear choice. One way or the other, you’re taking an unqualified risk.
Of course, If everyone else gets vaccinated against the disease except for you, you’re unlikely to get it, so you can get the best of both, a low probability of ever getting exposed to the disease, an no chance of suffering the side effects.
On the other hand, if everyone thinks that way, then the disease runs rampant and everyone is very likely to get it. This is, in a way, a Tragedy of the Commons game, in reverse. If you assume that everyone else will get vaccinated you are safe, but if everyone makes the selfish choice, then everyone suffers.
One could consider that there’s another benefit to getting the vaccination, and factor that in. You are protecting not only yourself, but everyone you know, and everyone that comes into contact with you. There is a social benefit with serious repercussions. It all depends on how much you care about your family and friends and the society in which you live.
When society is playing the game, the choice is obvious. If everyone gets vaccinated, no one will get the disease. A minimal number of people suffer side effects, but because of the large number of people involved, some small, random group is virtually guaranteed to suffer. But if no one or an insufficient number of people get vaccinated, the disease will strike hard and a large number of people will suffer.
For society, the choice is easy.
For individuals, the choice is difficult.
Fortunately, in our society, most people simply trust their doctor’s recommendation, and the doctors play the societal version of the game, not the individual’s version. Doctors do what’s best for everyone as a whole, so people tend to get their shots, and the ravages of disease are by and large contained.