The Game of Climate Change — Part 3

Start with Part 1 Here

Go Back to Part 2 Here

Mitigating Climate Change

It ain’t the heat, it’s the humility. — Yogi Berra

There are two big problems with the climate “debate”.  One is the tactics and “tricks” that people use, like putting certain “terms” into “quotes,” to imply that they aren’t “really” what the other side “says” they are (wink, wink).

Everyone knows the current “warming” is or isn’t, and that “deniers” and “warmists” aren’t, and that the “climate scientists” have “lost” our “trust.”

Right?  I mean, “right?”

The second problem is that too many people are playing it like a game, even though everyone takes it so seriously that discussions are quickly infused with anger and vitriol.  The problem that I see in the two sides is that each side measures victory by different standards, so they can never find any common ground.

The “anti” crowd would have no problem with mitigating climate change, if it weren’t for the fact that in their view it would completely “destroy” the economy and civilization as we know it.

The “pro” crowd would have no problem waiting and taking things carefully, one step at a time, if they weren’t convinced that there is no time, and that the repercussions of inaction will be “insurmountable.”


CO2So let’s frame it as a game – The Climate Game.  The game is not going to worry about whether or not warming is actually happening, even in terms of probabilities.  The game will be based on what we can or should do as a society in the face of that imperfect knowledge.

The other player is Mother Nature, a nasty, diabolical sort.  She’s tricky, vindictive, and tries to be unpredictable.  Her options are no warming at all, comfortable and inconsistent warming, lots of warming, and the reek and stench of the fires of hell.

Our side is played by all of the people, nations and economies of the world.

We’ll treat this as a zero sum game, where our own gain and loss are what really matter in our appraisal of the outcome.  In reality, Mother Nature always wins, one way or the other, in that life of some sort will go on, and the Earth will continue as a habitable biosphere, no matter how many creatures or entire species die off.  But for this game we’re only concerned with our own standing (that of the human race) when the game ends.

Points are roughly equivalent to dollars, effort, time, resources and lives.  We won’t use dollars, though.  I’ve heard people of late refer to their own personal economic standing as their hard won “treasure,” as in “blood and treasure.”  That phrase is popular among neocons today as an expression of the cost of wars already waged.  It’s used now much as it seemingly was in common use among leaders and politicians in the imperial atmosphere of the seventeenth and eighteenth centuries.  George Washington, Thomas Jefferson, Thomas Paine and Benjamin Franklin all used the term, having learned it from their British counterparts across the Atlantic.

So it’s appropriate here because it has that air of human sacrifice tinged with capitalist measure.  It sounds like a strategic term, used to evaluate the cold and realistic moves in a terrible, dangerous game.

It’s perfect – blood and treasure.  Our points represent some amount of blood and treasure.

Blood and TreasureThe moves that Mother Nature can make – moves that she will not reveal until long after we’ve made our own moves – are to leave the climate alone, or to warm it by varying degrees.  Again, we will try to avoid specific numbers, like 2°C or 3°C, since some people will argue that some warming is good, and others will argue about how much warming is good.

We’ll just label the options “No Change”, “Comfortable to Annoying”, “Dangerous”, “Seriously Dangerous” and “Catastrophic”.

Like all of the games that we’ve set forth, probability does not come into this analysis.  It’s becomes a question of payoff versus risk alone.

Our sole move at any time will be to either wait and study the problem for a period, or to begin to invest in renewable resources.  We’ll represent each choice by various periods of waiting.

This game will work from the assumption that if the game (i.e. the actual climate) ever reaches a danger point where the problem is obvious and dangerous, and requires a rapid, frantic, wholesale, and inefficient devotion of energy and resources, then that expense itself is treated as part of the cost of the outcome, and this game is at that point effectively over and a new game of  “Survive in an Altered World” begins.

But that is getting ahead.  For now, we want to phrase the game in today’s terms, in a way that seems realistic to anyone, in a very cold, analytical fashion.

This game also works, and this is very important because it is in fact the case, from the assumption that if we wait until we actually measurably perceive the warming, it is then too late.  The CO2 put into the atmosphere in the past and being added now will not manifest a dangerous temperature change until it is already too late.  The planet takes time to warm, just as it takes a person time to warm up after coming in from the cold.  The ocean itself is huge, as is the atmosphere.  The affects of warming take decades to accumulate, during which time, if we are adding more CO2 to the atmosphere, we are turning the thermostat higher but without immediately seeing that result.

So this game must be played completely blind.  An entirely “wait and see” approach is in effect counting on a particular outcome and simply ignoring other possibilities.

So the matrix (without the payoff values filled in) looks something like this:

Mother Nature
Humanity No Change Comfortable Dangerous Seriously Dangerous Catastrophic
Act Now
Wait 10 Years
Wait 20 Years
Wait 30 Years
Wait 40 Years
No Action

Assigning Values

You better cut the pizza in four pieces because I’m not hungry enough to eat six. — Yogi Berra

The most contentious and challenging part of creating this payoff matrix is the task of assigning values.  The first thing to remember in this process is that the payoff matrix has nothing to do with probabilities.  It’s not about what is likely, or more likely, to happen.  It’s purely a question of possible outcomes, payoffs and penalties.

The second point of contention will be the factors to consider in the costs.  Lives, money, average standard of living, lifespan, and personal security and freedoms all come into play, and all must be weighed on the same scale.  This is difficult, as it has much to do with personal values, but the American ideal of life, liberty and pursuit of happiness will be applied.  It was good enough for Thomas J., after all.

The third point of contention will be the relative benefit of continuing our current lifestyle unchanged, versus the actual future costs of belated mitigation or adaptation.  For example, if we were to needlessly abandon our current lifestyle, many would argue, there is a large price to be paid.  Others might argue that life would be better with a new lifestyle, but that argument will not satisfy most people.  On the other hand, the costs of moving entire cities, or massive continent sized irrigation projects to support entire groups of states with failing farmlands, must also be considered as far worse than the discomfort of driving a smaller, more efficient vehicle, or settling more often for locally grown foods or manufactured products.

The fourth point of contention concerns the size of our oil reserves.  The fact is that they are not unlimited, and we  will have to wean ourselves from fossil fuels eventually.  One could take the approach that the chance for climate change is simply providing an added incentive to address the issue now, before the shock of a shortage harms the economy.  One could also take the opposite approach, that since oil is going to run out eventually then action will naturally be taken through market pressures to move away from fossil fuels anyway, and considerations about climate change are unnecessary.

Either view is really irrelevant, however.  The point is that a cutover must be made, regardless of the “forcing” which causes us to take action.  For this exercise, however, we’ll ignore this.  We’ll focus only on what should or shouldn’t be done in the game of climate change.

The last point of contention will be the degree to which we should or would take action.  To me, this factor is beyond debate.  No nation or society on earth is going to destroy its economy or way of life in a rapid, drastic, single minded effort to eliminate fossil fuels, unless a preponderance of evidence guarantees that things will actually be far worse otherwise.  Human nature and the nature of modern democracies will very simply preclude precipitous action which instantly harms people’s lifestyles.

People will vote out politicians that push that agenda too hard.  They’ll vote with their wallets by buying what they want to buy, no matter what the future, as yet unknown penalty will be.  No one will ever be able to mandate drastic lifestyle changes.  No one, no nation on earth, will ever, ever “destroy” their own economy in an effort to mitigate climate change.  Arguments along those lines are, to put it simply, “alarmist.”  Such an eventuality will only happen if the effects of climate change become so great that the need to mitigate or adapt outweighs the damage to the economy, and that will only happen if proper, controlled mitigation comes too late.

That’s not to say that it can’t be done.  Huge sacrifices were made in World War II, by peoples of all nations.  Even in a nation as remote from the conflict as the United States, people proudly accepted rationing, men enlisted and trained, and women took factory jobs.  The U.S.A. was the only major player in the war to have virtually no civilian casualties, and except for a very brief period after Pearl Harbor, it was not even directly threatened by its enemies, and yet people made great sacrifices.

So it is possible, but that sort of sea change in human perception of events required something like the attack on Pearl Harbor.  Despite years of leadership by F.D.R., WW II required a shock that brought people to their senses, to get America involved, and to demand a sacrifice from them to accomplish a goal.

For the sake of argument, first consider the case where we act immediately with reasoned prudence.  There is no gnashing of teeth and hysterical wailing.  Economies do not collapse under the weight of instantly abandoning fossil fuels.  Countries simply do as economists are advising is wise and effective, such as investing 1% to 3% of each nation’s GDP into building a new energy infrastructure which is not based on fossil fuels.

CostsIt will cost money, and time, and effort that could instead be spent on making more Hollywood blockbusters or copies of DVDs or plastic Barbie jeeps (electric ones!).  It won’t cost jobs, because people will simply spend their time on one task (building a new infrastructure) instead of another (building plastic toys).  But if you want to look at it that way, you can say that your individual life will be less comfortable, because the price of plastic Barbie jeeps will go up, while you personally have nothing to show for the shiny new wind turbines that will ultimately feed your house the juice that would make the Barbie jeep go.

By contrast, if one waits until drastic action is needed, there will be additional, large prices to be paid.  The first will be that adaptation will cost much more than the 1% to 3% of the national GDP that early mitigation would have cost.  The second will be that at that point, adaptation must be accompanied by mitigation, but it would have to be done more quickly and aggressively, and under time pressure.  The third cost will be in then unavoidable human suffering as farms and businesses fail, communities fail, and the like.  In the worst case, there would be war, famine, and untold numbers of refugees.

The final cost will be in permanent losses to unrecoverable damage to the environment.

This last matter, again, is subject to individual values.  Some people care too much, while others flat out don’t care.  It’s very hard to measure that in blood and treasure.

So, given those factors, here’s a stab at a payoff matrix.  I’ve basically set the price of mitigating climate change now at one “blood and treasure” per year.  I have not added in any corresponding payoff for weaning off fossil fuels just because they’ll eventually run out, even though that would in fact be an economic benefit.

I’ve rather randomly added progressively large, additional costs for taking action too late.  Anyone can argue about the size of these additional costs, up or down, since they are as much based on personal values as economic factors, and the specifics of any outcome are in so much doubt.

You can, of course, make your own payoff matrix.  There are no rules here.  Trust yourself.  Just be fair to yourself in how you weight the various factors in each situation.  Dismissively pretending that the costs  for one situation or another will be arbitrarily high or low, without giving the scenarios proper consideration, does yourself, your neighbors, and your children an injustice.

Mother Nature
Humanity No Change Comfortable Dangerous Seriously Dangerous Catastrophic
Act Now -50 -50 -50 -100 -200
Wait 10 Years -40 -40 -100 -200 -500
Wait 20 Years -30 -30 -200 -500 -1000
Wait 30 Years -20 -20 -500 -1000 -5000
Wait 40 Years -10 -10 -1000 -5000 -10000
No Action 0 0 -5000 -10000 -50000

Making a Decision

If you come to a fork in the road, take it. — Yogi Berra

One of the complications of a game like this is that there is no dominant strategy, that there is no course of action which is indisputably better than any other by mere virtue of having a better outcome than any other course of action in any and all eventualities.

The decision here must be made without knowing Mother Nature’s play.

Before you play the game, try an experiment.  Keep the same values, or any that you came up with on your own, but change the column headings.  Instead of dealing with climate change as a planet and a people, let’s deal with heart disease, as an individual.  Your doctor has just looked at you, and all of your physical and lifestyle indicators and your family history, and suggested that you will eventually be at serious risk for heart disease.  You need to start an exercise program, the sooner the better in his eyes.  You could start now, or put it off for a while, but you won’t know how prone your body really is to heart disease until it’s too late to go back in time and reverse its course.  The thing is, your family and career are also very demanding right now, so making the time just isn’t easy.

Heart Disease
You Never Develops Mild Serious Dangerous Fatal
Act Now -50 -50 -50 -100 -200
Wait 2 Years -40 -40 -100 -200 -500
Wait 4 Years -30 -30 -200 -500 -1000
Wait 6 Years -20 -20 -500 -1000 -5000
Wait 8 Years -10 -10 -1000 -5000 -10000
No Action 0 0 -5000 -10000 -50000

The game is now one of making time to exercise, or simply living your life as you do, high in stress and calories.  You can’t know if you’ll ever develop heart disease.  It might never happen.  You might develop a low risk of a heart attack, or you might be ready for one within just a few years.

What choice would you make?

To me, this choice seems pretty easy.  The cost of exercising, even if I’m really not in any danger, is relatively minimal.  In the end, it will even have other benefits, such as having a higher energy level, a better appearance, and better self esteem.  In contrast, waiting even a few years increases the chance that I will die young.

More than that, in the event that I actually have little or nothing to worry about, the difference between waiting for any length of time is minimal, while the difference in waiting even just a few years in the worst case scenarios is dramatic.

Me, I exercise, starting today.

But the game we’re playing isn’t about one individual, it’s about billions.  The costs of mitigating climate change mean sacrificing some luxuries which we enjoy in such seemingly endless, trivial abundance today that they are of almost no true value to us.  Would you really, really care if you had a smaller DVD collection, or drove a car without four zone climate control, or if your TV screen was five inches smaller?

At the same time, the potential costs to both humanity and individuals are huge.  The fatalities, and the damage to society, may be staggering.  Forty to seventy million people are estimated to have died in WW II.  Entire major cities were destroyed, along with countless smaller ones.  Dresden.  Hiroshima.  Nagasaki.  So many people died in Russia and China that there is no accurate count.

WarThe worst effects of climate change will be no better.  Massive starvation due to major changes in precipitation patterns is a worst case possibility.  Man will certainly react to such pressures as he always reacts, with war.  The eventual (centuries from now) loss of many of the major cities of the world, as they almost all exist on a water front, will produce untold numbers of refugees, and demand the energy and resources to build anew, but this time without the benefits of fossil fuels.

Again, if the negative effects of climate change were to be inconsequential, or if modern science were in fact wrong on the entire matter, the difference in the cost of taking action now, versus waiting fifty or even only five years, is minimal.  There’s little distinction between the two courses.

If climate change itself is as dramatic and costly as current science indicates, or even worse, then the distinction between the options is decisively dramatic.  It makes the choice fairly clear.  Moving now, to make small, incremental changes, is far preferable to waiting until only major, expensive, and painful actions can be taken to reduce only a fraction of the probable damage.

Waiting to see what will happen is a decision in itself.  Inaction is action without commitment.  It is a choice.  It’s choosing to do nothing, and leaving one’s own fate to chance, except in this game it’s not only your own fate, but the fate of billions of people that share the planet now, and billions more who will follow and live in the aftermath of our game.

Filing for Divorce

Always go to other people’s funerals, otherwise they won’t come to yours. — Yogi Berra

There are other complications with taking action on climate change, even after making a firm, collective decision to do so.  The first is that action must be taken by society as a whole, and collectively by all nations, as well as individually by both people and corporations.  This is the Tragedy of the Commons again.  If one nation decides to cheat for a while, it hurts the others, but maybe not dramatically so.

But if one nation would cheat, then most might.  It’s human nature, but in so doing the world is by default choosing inaction over action.

The same logic applies to the actual, specific actions taken within a country.  It is in the collective interest to mitigate climate change, but it is in any individual’s or corporation’s interest to maximize one’s own profit, even at the expense of others.  Without an overwhelming sense of shared sacrifice, duty and honor among the populace, as the nations of the world experienced during World War II, there may be cheating to the point of failure.

Given this, it must be recognized that at a minimum, there will be friction.  Individuals, corporations, and whole nations will try as hard as they can to resist change.  Even though it isn’t really in their own best interests, they will put their personal, immediate interests above those of the planet as a whole, and even above their own long term futures.  There will be action, but with friction.  Five steps forward, one step back, more or less, depending on how committed people are, as well as how self serving they are.

Of course, in terms of countries, this will actually be a severe disadvantage.  The point will be reached where a fossil fuel infrastructure is not only dangerous to the planet, but also inefficient and expensive to maintain.  As more and more nations convert to more efficient energy grids, generation and delivery systems, fossil fuels will actually become a lame duck, and those nations that cling too tightly to that particular technology will actually fall behind.

Making it Happen

There are some people who, if they don’t already know, you can’t tell ’em. — Yogi Berra

Of course, saying “we have to do it” and actually doing it are two different things.  Figuring out how to get individuals, corporations and nations to cooperate, and how to find and punish the cheaters, is really the problem that we face today.  There’s no question that we must abandon fossil fuels, and the sooner, the better.  The question is how to do it, how to motivate, how to make the hard choices, and how to most effectively balance our efforts so as to cause the least distress, and to eliminate cheaters.

But giving up a drug habit, especially one that actually appears to be inexpensive, is going to be hard.  Doing it in a fair and consistent manner across the globe, involving different forms of government and different social and economic systems, presents a unique challenge… and would be the subject of another post.

The Desert of Liberty

Summing Up

I just want to thank everyone who made this day necessary. — Yogi Berra

It’s tough to make predictions, particularly about the future.  — Yogi Berra

It ain’t over til it’s over. — Yogi Berra

Unfortunately, this last item, knowing when it’s over, in the climate game, Yogi got wrong.  A lot of people, those that would rather that climate change be a non-problem, see the current warming, around 0.5˚C to date, as insignificant, or at worst not a real problem or anomaly, and at best, maybe even a good thing, with potential benefits like higher crop production and milder winters.

But if the science is correct, then the temperature you will get in the end is not what you feel today.  The CO2 that is in the atmosphere now will take an unknown number of decades to manifest itself as a temperature change and to reveal the final equilibrium temperature of the planet.  Among many other factors, the volume of water on the surface of this planet, and the time it will take to heat that body of water, will hold temperatures down and make the transition to a “brave new future” slow, if steady.

It’s like turning up your thermostat to 90 degrees and then breaking it at that setting.  Your house doesn’t heat to 90 degrees instantly.  It takes quite a while.  But with the thermostat broken, you have no way to stop it.  Adding CO2 to the atmosphere is just like that.  Every bit we add turns the thermostat up, and it can’t be taken out once it’s there – the thermostat can’t be turned back down.  But how hot it will get as a result of this CO2 is not reflected in this year’s, or next year’s, or even the next decade’s temperatures.  It’s going to take a long time to see how far up we’ve pushed the Earth’s thermostat.

Mother Nature doesn’t have to show her cards until long, long after we’ve shown ours, and by then it’s too late to change our moves.

So, with deference to Yogi’s usual wisdom, in this case it’s over long before it’s over.  Going back to baseball for an analogy, we can’t count on a two out, bottom of the ninth rally in this game.

And now the leather-covered sphere came hurtling through the air,
And Casey stood a-watching it in haughty grandeur there.
Close by the sturdy batsman the ball unheeded sped-
“That ain’t my style,” said Casey. “Strike one,” the umpire said.

The Desert of Liberty

The Game of Climate Change — Part 2

Start with Part 1 Here

Depressing Games

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.

The World Oil GameOn 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.

The World Oil End GameInsurance, Vaccines and Preventive Care

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:

Your Choice
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.

The Vaccination GameOf 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.

Next Installment — Mitigating Climate Change

The Game of Climate Change — Part 1

An Important First

He’s an often quoted icon of American sports, an Italian American great, known for his quirky, folksy, and seemingly ignorant yet poignant wit.  He has appeared in more World Series games than any other player, was a fifteen time all-star, and voted American League MVP three times.  He was a leader, too, not just a player, managing seven teams into the World Series, and winning it three times.

Who could have known?  The sports writers clearly didn’t know.  The fans didn’t know, or the other players.  He himself didn’t even know it, at least not consciously, and he probably still doesn’t.  But Lawrence Peter “Yogi” Berra may have been the first and most important climatoleconomist, ever.

The future ain’t what it used to be. — Yogi Berra

Game Theory

People love games.  Sports, video games, board games, card games, parlor games, and gambling with small or large stakes.  Baseball itself is known as The Great American Pastime.  It would be hard to find someone that didn’t enjoy a game of some sort.

If people don’t want to come out to the ball park, nobody’s gonna stop ’em. — Yogi Berra

Okay, people also like to win at games.  But frustration with losing teams aside, people love games.

Games of Chance

Which is good, because we learn a lot from games.  We learn how to compete, how to manage our resources and our future, and we learn better how to survive.

Sociologists, economists, political scientists and even philosophers make use of a fascinating branch of applied mathematics called Game Theory.  Game theory attempts to structure the parameters and outcomes of competitive and even cooperative strategic situations – a complicated way of saying “games” – with the goal of studying the decision making processes of the players, and if possible defining the best strategies for each player.

A simple grid, a payoff matrix, is designed with a box for each possible outcome.  In a two player game, one player’s choices are listed in the columns, while the opposing player’s choices are listed in the rows.  Numbers are placed in each intersecting cell to represent the value of the outcome, as in the meaningless and random example below:

Player 1
Player 2 Action A Action B
Action C 5 -3
Action D 2 10

Let’s examine a simple real world example to demonstrate more clearly – baseball, or rather, one specific part of a baseball game.

On the off chance that you’re not familiar with baseball, both pitching and batting are something of a guessing game.  Visualize the duel between a baseball pitcher and the batter.  The pitcher wants to select the best pitch to get an out, or at least a strike, while the batter wants to guess the pitch that is coming in order to improve his chances of getting a hit.

A curveball comes in more slowly than a fastball, and it actually moves from one side to the other, seemingly approaching from one direction, then veering away in another.  If a batter isn’t ready for it, and swings, he will either miss or just might make contact, but any hit will be weak and off balance, probably resulting in an out.  But if the batter is ready for the pitch, because it’s coming in more slowly than a fastball, then he can get a hit, but because of the curve in the path of the ball, he’s not likely to get a really good hit.  A single (a chance to take one base) isn’t out of the question, though.

On the other hand, if the batter is looking for a curveball and a fastball whizzes by, he’s pretty much going to swing late or not at all, and take a strike.  If he’s instead looking for the fastball, which comes in straight and hard, and if he can connect, then he has a chance of hitting it equally hard in return and getting more than a single out of it.

Baseball and Games of Chance

We’ll assume for our little game, for simplicity, that the hitter’s skill is very good, almost infallible, and that the pitcher always throws strikes (i.e. balls that the batter must swing at to avoid a strike, and that the batter might hit if he tries).

In game theory we could represent this pitcher-batter-baseball guessing game like this:

Pitcher throws…
Batter looks for… Curve Fastball
Curve single strike
Fastball out double

Except that this is mathematics, so we translate things into numbers, like this:

Pitcher throws…
Batter looks for… Curve Fastball
Curve 1 -1
Fastball -3 2

Here, a 1 is a single, a 2 is a double, a -1 is a strike, and a -3 is an out (the equivalent of 3 strikes).  Positive numbers are good for the batter, while negative numbers are good for the pitcher.

There’s only one number for each result because this is what is known as a zero-sum game, meaning that what is good for one player is bad in exactly equal measure for the other player.  Most games that are played for fun, and most competitive games, are zero-sum games.  For instance, in chess, the loss of any piece is exactly as bad for the player losing the piece as it is good for his opponent.  In betting, a winner wins exactly as much money as the loser wagered (unless a bookie is involved, but then that’s not a simple game anymore, it becomes economics, which is very interesting but is not our topic – yet).

For simplicity, we’ll avoid probabilities and the chance that different things may happen different times, like the chance that the batter will squeak a hit out of an unexpected curveball, or get a triple or fly out instead of a double when connecting with a fastball.  We’re interested in the decision making process, so in our game there’s only one, definite outcome for any combination of pitcher/batter choices.

Partly because it is a zero sum game, and because each choice has good and bad returns, there is no optimal strategy for this particular game, and no reason or tendency for the players to keep making the same choices (known as a Nash Equilibrium) in repeated play.

Play the game against yourself a few times, by playing both sides, or using the roll of a die or a coin toss to decide the actions of the other player.  Once you have a feel for it, read on.

Studying the payoff matrix, you can see that a conservative pitcher could choose to throw more curve balls, figuring that his risk is lower (giving up singles instead of doubles when the batter guesses correctly) and his return is higher (getting an out instead of a mere strike when he guesses correctly).  But a batter is likely to take the same approach, risking only strikes instead of an entire out by looking for curve balls.  In this event, the batter would get repeated hits, so the pitcher can’t afford to continuously, thoughtlessly throw curve balls.  Once the pitcher starts to throw some fastballs, the batter can’t simply keep guessing curve, and the pitcher likewise can’t afford to continuously throw fastballs (or the batter will adjust, and hit a lot of doubles, scoring runs).

Fun Games to Play

Of course, the real fun for the mathematician (or sociologist, or climatoleconomist) comes from considering unusual games, and using game theory to determine what the best strategy would be in perplexing situations.

We made too many wrong mistakes.  — Yogi Berra

The most common introductory example used in game theory is known as the Prisoner’s Dilemma.  The idea is that two criminals have been arrested, separated and interrogated.  Each of them is being made the same offer; rat out the other guy, and you’ll get a reduced sentence.  Of course, without a confession, there’s not much evidence, so if both stay quiet, they’ll only do 1 year in prison.  If they both confess, all deals are off and they’ll get 5 years each.  But if one squeals on the other, while his buddy stays loyal, then the rat goes scott free while his buddy gets 10 years.

Here’s the payoff matrix:

Prisoner 2
Prisoner 1 Silent Squeals
Silent 1,1 10,0
Squeals 0,10 5,5

In this matrix there are two payoff numbers.  The first is the number of years that the first prisoner gets, the second is the number of years that the second prisoner gets.  This is not a zero-sum game, because what happens to one player is really irrelevant to the other.  They can each win or lose in different amounts.  The goal for each player is to minimize his own sentence*.

*After all, there is no honor among thieves, lawyers, and politicians, right?

Again, use a coin or dice to play it yourself.

PrisonThis game has a surprising, dominant strategy, which is to squeal, even though both players would be far better off keeping silent.  Since one player can’t be sure what the other player is going to do, it would always be best to squeal.  If the other guy squeals and you don’t, you’d do ten years.  But if you squeal and the other guy squeals, you’d only get 5 years, and if he’s stupid enough not to squeal, you’ll go free.  Your own result is always better if you squeal.

So squealing is always without question the best strategy.  Assuming both players have thought this out, they can expect to spend five years in prison, and if they are smart they’ll use the time to brush up on their game theory.

Frightening Games

We’ll look at two other games of note, before we begin to apply game theory to current events.

In theory, there is no difference between theory and practice.  In practice, there is. — Yogi Berra

The first is called Global Thermonuclear War.  This one covers the Cold War between the U.S.A. and the U.S.S.R.  Each country had thousands of nuclear armed missiles aimed at the other.  If one were to launch, and the other didn’t, the reluctant nation would be annihilated and the other would rule the world.  But if both launch, the world would be destroyed.  Finally, if neither launches, there is peace, in which no one wins a war, but no one loses.

Global Thermonuclear WarFor the sake of this game, it is assumed that if one side gets in a first strike, the other will not have time to launch, so the decision must be made before you are entirely certain as to whether the other side has launched their missiles or not.  Imagine that it’s 3 AM, when General Jack Ripper calls.  He says it’s too early to tell for sure, but he thinks the commies have fired their missiles in a massive strike.  Does he have permission to fire back, and blow the commies all to hell?

Here is the payoff matrix, where the first number is the payoff for the U.S.A. and the second number is the payoff for the U.S.S.R.

U.S.A. Launch Wait
Launch -∞,-∞ 1,-1
Wait -1,1 0,0

If neither side launches and peace is maintained, the status quo remains and neither side gets any points (0,0).  If one side launches and the other doesn’t, the other is destroyed (-1) while the winner is left in control (+1).  But if both sides launch, in the combined nuclear holocaust the entire world is destroyed (represented by a -∞ for both players).

This is not a zero-sum game, because while in the event of war one side wins and the other loses in equal measure, and in the event of peace nothing changes, but in the event of Armageddon, both sides lose everything.

In this game, there is no obviously dominant strategy.  The question becomes one of how much you are willing to risk.  You could argue that the only way to win is to launch, but you’d be risking everything.

Consider your strategy in a scenario where you get to play this game repeatedly.  Imagine that even if you lose one nuclear war, over time you rebuild your country and so get to play again.  Then your average return is better if you do not launch (-0.5 per play, instead of -∞).  You’d have to play forever to be as badly off as if you both launched just once, so seemingly the best plan, if you go with best average return, is to wait.  If both sides use this strategy, then the best possible outcome for both sides is achieved and peace is continually maintained.

Interestingly, there is a Nash Equilibrium in both sides launching.  That is, if you could somehow play the game repeatedly, once one player decides to launch, the other player should anticipate that the player will launch again, and should decide to launch as well.  Once both players are launching, it would be a mistake to change strategies.  The best you could do would be to break even, but only if the other player decided not to launch at the same time.  Of course, as the game is structured now, once both players launch at the same time, the game ends, but this is all just theory, and the point is to think about thinking.

We could modify the game somewhat.

If you instead declare that any nuclear war is final, and your concern is solely for your own country, one could argue that the payoff (loss) in losing a nuclear war is also -∞.  That is, there’s no difference between losing a nuclear war and the end of the world if you don’t care about the entire world.  In that event, the payoff for waiting while the other country launches is not merely -1 but -∞.

That payoff matrix looks like this:

U.S.A. Launch Wait
Launch -∞,-∞ 1,-∞
Wait -∞,1 0,0

This would change your approach to the game in that your fate is entirely in your opponent’s hands.  You will lose everything if he launches, no matter what you do.  Given that fact, you might as well launch.  If he doesn’t launch, he loses and you win.  If he does launch, you both lose.  This is much like the prisoner’s dilemma, where you might as well do the “bad” thing, because you can’t trust your opponent to cooperate.

Of course, in real life this game never played out any way but peacefully, because world leaders never saw, understood and used game theory, and this payoff matrix in particular.  World leaders are always smart enough to take easier courses in their college days than applied mathematics, or if they did, they cut class a lot*.

* Actually, it’s because of a lot of reasons, including the fact that after you’ve played the game of Global Thermonuclear Warfare once, you don’t get to go for best two out of three.  Whatever the ultimate reason, we’re thankfully here to talk about it today.  Humanity successfully dodged the first deadly bullet that it aimed at itself after inventing the nuclear bomb, and then decided it was such a good idea that a lot of different, competing countries should have a lot of nuclear bombs, too, all at once.

Next Installment — Part 2 — Depressing Games…