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There is a field in economics known as Game Theory. This field tries to break situations down into simple mathematical models to determine what a "rational" person would do. In this article, see how game theory can be used in life and game design!

The following is a reproduction, and was originally posted on March 24, 2018. The original article, and many more, can be found at RemptonGames.com

Hey everybody! The last few weeks I have been writing my annual review articles, and haven’t been able to put up any new game design content. That, however, changes today. As promised, today is the third entry in my series “Game Design in Real Life”, where I take a look at how game design can be used to improve the world, or what the world can teach us about game design. If you haven’t read the previous entries about design lessons from Disney World and Gamification, you can find them here and here.

Today, I am going talking about game theory, but not in the way that I usually do. Instead, I am going to be talking about the academic field of game theory. Specifically, I am going to be looking at one common example of this field known as the prisoner’s dilemma.

That’s just a Theory!

Before I jump into the prisoner’s dilemma itself, first we need to answer the question – what is game theory? From an academic perspective, game theory is basically a way of trying to predict or model human behavior using mathematical game models. These game models are usually highly simplified, and have very strict rules and restrictions on what players are allowed to do.

While people have been discussing games for millennia, and theories that fit within the current idea of game theory have been discussed since the 18th century, this field didn’t really begin as an academic discipline until the late 1920s. Even then the field remained in relative obscurity until the 1950s, when it exploded in popularity.

Since then, game theory has been used in applications ranging from economics to psychology to politics, all in an attempt to explain human behavior using games. It has even led to a number of Nobel prizes in economics! However, while this field seems to be very valuable to academic study, can it actually tell us anything about games?

In a Predicament

To find out, let’s take a look at a very common example of game theory, known as the prisoner’s dilemma. In this scenario, there are two criminals who have been captured by the police. The police have some evidence against both of them, but not enough to charge them for the full crime. At best, they would probably be able to convict them on a smaller, less serious crime. Therefore, the arresting officers decide to separate the two suspects and offer them a choice.

Both suspects get the exact same offer, and it goes something like this. If neither suspect provides evidence against the other, they will both be convicted on the lesser charge and receive 1 year in prison. If only one suspect provides evidence against the other, the one who provided the evidence will get to walk free, while the other gets charged with the more serious crime and gets 3 years in prison. Finally, if both suspects betray eachother they both get 2 years in prison.

Also, because this is an academic model, there are a number of additional constraints. These constraints include the fact that neither player has any loyalty to the other, and that there is no risk of retribution for being betrayed. Also, the unspoken assumption is that every player is a rational person who wants to maximize their own well-being.

What would you do in this situation? Well, if you stick to the constraints of the problem there is really only one option – each prisoner will betray the other. After all, their only concern is minimizing the harm to themselves, and betraying their partner will always provide a better outcome for them.

How can this be? Why would both prisoners betray the other if a better outcome would be for both of them to stay silent? The answer comes from self preservation. Neither prisoner knows what the other person is going to do, so each has to evaluate two different possibilities. What happens if my partner betrays me, and what happens if they don’t?

If your partner doesn’t betray you, then you have two options. You could stay silent as well, in which case you serve 1 year, or you could betray them, in which case you serve no time. In this case, it makes sense to betray your partner. But what if they do betray you? Well, in this case you also have two options. If you betray them back then you serve 2 years, while if you stay silent you will serve 3. Once again, it is a better outcome for you if you betray them.

From a strictly logical perspective, this outcome makes sense. However, given the huge number of constraints placed on this problem it makes for a very poor model of real human behavior. Real humans do feel loyalty towards eachother, and the risk of retribution is a very real possibility. Also, and this is probably the biggest issue with this model, it assumes both players to be purely driven by logic, which is extremely unlikely in a situation like this where both players are facing potential prison sentences for their choices. In reality, all of these different factors will come into play, and many people will actually end up cooperating, even though it is considered a “sub-optimal” solution.

Finding the Point

If the prisoner’s dilemma cannot always be used as an accurate predictor of human behavior, then what is it even good for? Well, although the situation itself may seem somewhat contrived, there are actually a number of different real-world situations where this type of problem does occur.

The business world is a great place to find examples of the Prisoner’s Dilemma because, unlike with human beings, many of the constraints actually apply. Businesses tend to have no real loyalty to eachother, and are usually driven entirely by their own benefit – specifically, profit. Therefore, there are a number of situations where different businesses must make the same decisions separately, and often result in outcomes that are worse for both of them.

One example of this could be clothing companies moving factories overseas. If no companies did this, then the relative prices of clothing would stay roughly the same. Clothes would be more expensive overall, but because all options are remaining at this higher price it doesn’t change the market much. However, if only one company moves their factories then they get to solely benefit from this decision. Every other clothing company loses money, while they are making more profit due to cheaper production costs. In the end, while it may be better for the national economy if no businesses moved their factories, the risk of becoming non-competitive is just too high.

Once you start looking for them, examples of the prisoner’s dilemma start to show up everywhere. From tax policy, to the use of performance enhancing drugs in sports and e-sports, to the nuclear arms race, all of these different situations could be examined through the lens of this model. This can even be seen in popular culture – there was a short lived game show known as “Take It All” which used the prisoner’s dilemma as one of its mechanics, and the Joker’s plot with the two boats could be seen as a suitably twisted version of a prisoner’s dilemma.

This situation can actually occur in real games as well. Many board games involve an element of verbal agreements, such as a temporary truce in a war game or an economic game where you make a deal in exchange for future profits. In these games, both players benefit from the deal, but they benefit more if they are able to double-cross their opponents. This leads to many situations where it may become necessary to break an agreement that was made in order to win the game, and whoever breaks it first gains the advantage.

Until Next Week!

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