Darwinian Evolution
Game Theory
It’s been awhile since we’ve added to the Toolbelt of Knowledge, perhaps because there is so much we can explore in the space of ideas with what we’ve already covered. Today, I’ve decided to add to the longtime-lonely Theories category with another theory that can show us a new perspective on behavior, actions, and ethics: Game Theory.
What is Game Theory?
By its name, we might think Game Theory is a theory of games. It’s not, though. Most commonly, Game Theory is described as a theory of goals, outcomes, and strategies, though it can also be thought of as a theory of acting in accordance with our values. Game Theory is a theory of choices and consequences, actions and effects. The reason it is called “Game Theory” instead of “Strategy Theory” or “Choice Theory” is that games are structured with rules and goals for the players, and so it is easy to apply Game Theory to games. In this blog post, any time we mention “games,” we mean game theoretic systems, unless it is obvious by the context that we are talking about games in the fun-and-games sense.
There are three elements to a game theoretic system: Agents, the people, animals, AI programs, etc. who make decisions; the choices available to them; and the predicted outcomes of each combination of choices. The outcomes are usually written as a list of numbers, such as (3, 10, -1, …). Each number represents how satisfied each person is with the results.
You might see a problem here: in a game, this can represent the number of points each player ends up with, but how does it apply to the rest of life, where outcomes are not so easily quantified?
The answer, in my view, is that Game Theory should not be considered a theory of winning, but a theory of actions and consequences. Instead of numbers, we might put emojis representing how each person feels about the results. Or, we might directly represent the outcomes, rather than trying to quantify them. This can make it more difficult to compare the outcomes, but there are still times when we can comfortably say A is better than B, such as if A includes intense happiness and B includes despair.
Let’s look at some of the concepts of Game Theory, and some of the systems we can apply it to.
Positive-Sum, Negative-Sum, and Zero-Sum
There are three possible ways the total amount of “points” at the end can compare to the total amount at the beginning. If there is more at the end, it is a positive-sum resource; if there is less at the end, it is a negative-sum resource; and if the amount at the end is the same as the beginning, it is a zero-sum resource.
A note on terminology: you have probably heard the terms “positive- etc. sum game” instead of “positive- etc. sum resource.” A _____-sum game is more tied to the way the agents look at the game. For instance, if we say someone is “playing a zero-sum game,” it means they are trying to gain more by taking from others, rather than trying to increase the pot for all.
To illustrate each of these resource types, let’s look at the economy of a hypothetical island nation. This nation is self-reliant, it doesn’t trade or interact with anyone else.
The people of this island want to make it thrive. So they work the farms, build houses, mine for minerals, chop down and plant trees, educate their children, and all the other things a society needs in order to thrive. At the end of the year, they have more seeds, more knowledgeable people, more metal and wood and other resources than when they started with, and they are ready to start the next year and continue to reap increasing returns. This is a positive-sum game.
The land on the island is a zero-sum resource. There is a fixed amount, so if every acre is owned by someone, the only way for a person to acquire more is to get it from someone else.
And finally, the island’s coal supply from the coal mine is a negative-sum resource. The best use for coal is to burn it for electricity, but the more the nation uses, the less there is left to use. In order to continue to thrive in the long term, they must get off the negative sum game of coal power and find a positive sum game with renewable energy sources.
Short, Long, and Infinite Games
There are essentially three ways to strategize about a game-theoretic scenario. Short games are where we try to score as many points (metaphorically or literally) as possible as quickly as possible. A 100-meter dash is a short game; the goal is to get to the finish line before as many of your competitors as possible.
In a long game, the idea is to bide your time, waiting for the right moment to make the pivotal move. In a long game, we make short-term sacrifices for long-term payoffs. Chess is the archetypal example of a long game, as the ultimate goal is to trap the king, and it is common practice to sacrifice one’s own pieces in order to trap the other player in a snare.
An individual person’s life is a long game. The ideal life, according to present-day America and some other places, is to work hard at education, take out some loans for college, get a job, take out some loans for a car and a house, and slowly work off our debts until we break net positive and start accumulating wealth later in life.
An infinite game, on the other hand, is one that doesn’t end. The goal of an infinite game is to stay in the game as long as possible. Those who score points in infinite games are not people, as people have finite lifespans, but longer-lived things like countries, religions, and social causes.
Wars may end. Civil rights may be won. Oppressive regimes may be toppled. But their ripple effects continue, and in order to understand the way things are in the present and move toward a better future, we must study the past. Though the threads of history change, none of them end. History is a collection of infinite games.
Dominant Strategies
Sometimes, a single action can lead to positive results for all possible outcomes. These are called dominant strategies. Let’s look at a few examples.
Suppose we have a scenario where there is one choice: to light a candle or not to light it, and one risk: the candle might fall over. There are four possible scenarios.
1. We do not light the candle, and it does not fall over.
2. We do not light the candle, and it falls over.
3. We light the candle, and it does not fall over.
4. We light the candle, and it falls over.
If the fourth outcome happens, the house catches on fire, but in the other three outcomes it does not. We notice that if we do not light the candle, there is no outcome that results in a house fire. So if our goal is to not have a house fire, the dominant strategy is to not light the candle.
Another example can be found in cooking. If we are cooking a pan full of food, such as stir fried vegetables, we want to cook every piece equally on all sides. The surefire way to do this is to flip each piece individually. But if we do that, it takes too long, and by the time we’re done with the last piece, the first one is burnt. A better way to get it all cooked evenly is to stir the whole pan, making all of the pieces tumble around. Instead of having to plan each time exactly how to deal with each piece of food, stirring the pot or pan works every time. It is a dominant strategy.
Of course, in real-life situations it is often hard to find dominant strategies, since there are usually a very high number of factors and choices. Still, we can use this concept to look for strategies that have high probabilities of leading to good outcomes for a wide variety of ways a scenario might go.
Instrumental Goals and Ultimate Goals
There are two types of goals we might have in game-theoretic scenarios. An ultimate goal is what we are after, the outcome that would give us the most satisfaction from the game. Along the way, we pick up instrumental goals, things that help us achieve our ultimate goals.
Suppose my ultimate goal for today is to finish writing a blog post. In order to do that, I pick up a number of instrumental goals. I make coffee, because caffeine helps me think faster and more clearly. I eat food for similar reasons. I cross the street carefully, because it would be very difficult to finish my post if I am in the hospital or dead.
Of course, there are other reasons to do these things; other games being played. I’m playing the long game of life, in which writing is my major marketable skill, and finishing blog posts is an instrumental goal in service of the goal of making a living as a freelance writer, which is an instrumental goal in service of the goal of pursuing my passion as a science fiction author, which is . . . You get the picture. It’s not always clear what one’s ultimate goals are, or if their web of instrumental goals loops back on itself, or goes on forever.
The distinction between instrumental goals and ultimate goals comes from artificial intelligence research, not Game Theory. But they are useful in the same way as the rest of the ideas we’re looking at today, so I thought it made sense to add them to the Game Theory bundle.
Prisoner’s Dilemmas
Most of us are taught that being selfish is bad, and that we should share and be kind to others. Game Theory has several mathematical models supporting these ideas, the most well-known among them the prisoner’s dilemma. Abstractly speaking, a prisoner’s dilemma is any situation in which people acting in their best interests at the expense of others makes things worse off for everybody.
I won’t use the famous prison example today; you can find a million explanations of it with a quick google search. Instead, let’s look at another example: water rationing. Suppose there is a drought, and a town that usually has plenty of water for everyone starts to run low. The water supplier puts out a public notice, telling everyone that if they don’t limit their water consumption, the supplier will have to start temporarily shutting off the water for several hours at a time.
Each person is faced with the following conundrum:
1. Limit water and there is no shutdown.
2. Limit water and there is a shutdown.
3. Do not limit water, and there is no shutdown.
4. Do not limit water, and there is a shutdown.
In either case, whether or not there is a shutdown, an individual gets to use more water if they don’t limit their own consumption. Therefore, the dominant strategy is to ignore the public advice and use as much water as they want.
However, if too many people make this choice, the water will be rationed by the supplier, making things worse for everyone than if they had all limited their own water consumption. Hence the dilemma: the best possible outcome requires everyone to make the choice that is not the best for themselves.
The way to deal with prisoner’s dilemmas is through trust and self-sacrifice. We have to make the decision that is bad for ourselves, trusting the others to do the same. This is one of the reasons why it is important to treat others well and build relationships, even for people who only care about themselves. If everyone makes the hard choice to do the right thing, everyone ends up better off than if someone makes the selfish choice.
When considering things like political issues, our plans for our own lives, how we treat others, and stuff like that, it can be helpful to consider the questions from a game theoretic perspective. I may feel like this choice is right, but will its consequences actually line up with my values? Am I treating this situation like a zero-sum game, when it could be taken as a positive-sum game? Could a little sacrifice and trust on my part lead to a better outcome for everybody? These questions put things in a new perspective, and can lead to wiser choices and better outcomes.
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