One of my favorite pastimes and potential field I would want to study is game theory. I always liked how math and psychology combined to create a topic that could put numbers into human behavior. (Sounds like something a detective would say.) One of the first examples I had in game theory was the Prisoner’s Dilemma. I think I first encountered a variation of this when watching Brain Games. Here is the premise of the prompt:

Imagine that you and a partner have been arrested for a crime you have committed, like say, robbing a bank. Now there are two things each of you can do. You can either choose to plead the 5th and not rat out your partner, or you can snitch on them, and have them take a higher sentence. Keep in mind that your partner can do the exact same thing. Different variations have different lengths of sentences, so I will just use random numbers. There are four permutations that can occur with each of your and your partner’s decisions. The first is if you both decide to remain silent, you both would only get a 2-year sentence, if you snitch on them and they don’t, you would get a 1-year sentence, but your partner would get a 5-year sentence, and the opposite is true if they snitch on you but you don’t. And finally, if you both snitch on each other, you would both get a 3-year sentence. 

 

The variation I saw on Brain Games was a much kinder version in which you and another person have the same choices but about splitting some money. If you both agree to split you both get half, if one agrees but the other disagrees, the one who disagrees gets the money, but if both disagree, no one gets the money. This question started the rabbit hole I fell down from learning about human behavior in my young mind who was obsessed with detectives. (Here is the TED-ED video because the Brain Games one is blocked.)

I liked this problem originally because it started my interest in psychology and it had a lot of numbers in it. As I learned about the main problem being the Prisoner’s Dilemma and the variations about it, it got me thinking about the questions most game theorists have: How can we statically predict human behavior? 

 

The field of game theory is putting numbers into everyday actions. So, like any science project, we start with a hypothesis. Say, we hypothesize that 35% of the time, people will snitch on their partner. This would result in a table looking like this:

	Defer	Snitch
Defer	42.25%	22.75%
Snitch	22.75%	12.25%

We would then say, most likely, both prisoners would defer and get the same light sentence. Then we would test this hypothesis with an experiment. So then we would ask, say 100 random people that represent a larger group and ask what they would do in this situation. We don’t need to pair them up like in the Brain Games example, because the only data we need is how often someone defers or snitches, and then simulates the pair up randomly. Then we compile our data and take note of our observations. What we learned from this experiment is that 71 people chose to defer while 29 people snitched. Based on our data, our hypothesis was close, but we realize that more people would rather defer. So this is our data table now:

	Defer	Snitch
Defer	50.41%	20.59%
Snitch	20.59%	8.41%

What our data shows us, is about half the time, random people who pair up together will both defer. Now if this experiment took place in Naperville, which was our larger group, I can predict that about half the time, when random people in Naperville are put in this dilemma, they would defer, and both snitch less than 10% of the time.

 

Now what’s interesting about this dilemma is that you can change the prompt to yield different outcomes. For example, say instead of getting 2 years if you and your partner both defer, you get 3 years, and if you snitch and your partner defers, you are freed, but your partner still gets 5 years, but if you both snitch, you both get 4 years. So let’s create a new hypothesis. This situation seems more like a high-risk, high-reward situation so I think about 40% would choose to snitch. Now, having the same type of experiment, we will collect data. This is our new data table after we learn that 48% of people choose to snitch.

	Defer	Snitch
Defer	27.04%	24.96%
Snitch	24.96%	23.04%

What this suggests is a more even split between the four options. So, when there is a riskier option that may benefit more, people are more likely to take it. This is a basic study of psychology, and with the data we have collected, we can use math to predict future outcomes. Seeing the nuances change the outcome of the prediction is why we use math in game theory. 

 

But we can collect even more data. By asking the participants a series of demographic questions, we can determine what type of person would answer the question with a specific answer most of the time. For example, we can use the experiment to see that more friendly and passive types of people would defer 88% of the time and more aggressive people defer about 24% of the time. If we look at the data table for this, we would see a particular column has the largest value:

	Defer (Passive)	Snitch (Passive)
Defer (Aggressive)	21.12%	2.88%
Snitch (Aggressive)	66.88%	9.12%

With this, we can see how putting people non-randomly effects skews the predicted outcome. In this example, about two-thirds of the time, the passive person gets sent to jail while the aggressive person gets freed.

 

So, what did I and other game theorists learn from this? Me being new to game theory learned how to take data and learn all sorts of variations and variables into account when taking data. But a takeaway from the last example we can learn is that certain types of people may be more successful than others when avoiding one’s fate. Even though it may seem like common sense that aggressive people will get their way over passive people, we now have the math to back it up. In this case, the independent variables would be the time served, and the dependent variable would be the percentage of people who would defer or snitch.

 

Look at all the math we’ve done! This is why I got interested in learning about game theory. It has such a perfect balance between math and psychology that I can’t help but want to explore it more. Of course, there are more prompts and dilemma’s to explore, but I hope you all learned a little bit about the Prisoner’s Dilemma and its variations of it. Now that this detective has gotten some background on criminals and prisoners, we can move on to solve the main case, but first, we must take a look at the development of the side quest…