Transcript for:
Game Theory 101 Lecture Notes

Hi, I'm William Spaniel. Let's learn some game theory. Today we're going to be introducing this series, Game Theory 101, and over the course of the next 30 to 40 videos we will be learning basic introductory game theory. So let's get to it.

First, let's talk about what game theory is. Game theory is simply the study of strategically interdependent behavior. Strategic interdependence is simply a way of describing situations where what I do affects your outcomes, and what you do affects my outcomes. These types of situations could be just about winning and losing. I know when we think of the word game, immediately we think about types of games where I'm trying to beat you and you're trying to beat me, and only one of us can win and only one of us can lose.

But game theory allows us to be a little bit more broad with what we're doing here. Our framework can be much more general than that, and so we can talk about situations where we're both trying to help each other win, and also situations that are somewhere in between, where we have incentives to work together, but also incentives to beat the other guy in some sense. And game theory is going to allow us to study that all in a single way.

It's really useful. And to allude to what I'm going to talk about next, why even bother with these 30 to 40 videos? Because game theory will be time consuming.

It's going to be logically demanding for us to learn, but there is a light at the end of the tunnel. There is a reason, actually I'm giving you two reasons why we should bother doing this. First, if we're talking about theories of interactive behavior. The logic of strategically interdependent situations can get extremely complicated and extremely fast. So if we're going to develop logically sound theories, we need some sort of accounting standards to make sure that what we're saying actually follows from our assumptions.

And game theory gives us these accounting tools. So that's one reason why we should study them. Now a more practical reason to study game theory is that understanding these sorts of models allows us to quickly draw parallels from one situation to another. And once you have this sort of thing down, once you've spent the time, invested the time, learning the basics of game theory, it allows you to connect these strange situations together, which in turn allows you to think on your feet much better than you can today.

In fact, there is a particular time that I will discuss later in chapter two of this lecture series where I was in trouble with the police and my knowledge of game theory allowed me to sort of get out of that situation with very little cost to myself. So we'll talk about that and why it was really useful to me once we get there. Now, this lecture series will cover three chapters in total. We're going to start out with the basics.

So in chapter one, we're going to be talking about simultaneous move games. These are games where the players essentially have to come up with their strategies independently and without observing what the other guy does. So some examples here include soccer penalty kicks, prison interrogation when you're isolated from your fellow criminals, and deciding whether to stop or drive at a stoplight.

Now, over the course of this chapter, if you're interested in seeing what we're actually going to cover, we're going to talk about strict dominance, iterated elimination of strictly dominated strategies, pure strategy Nash equilibrium, best responses, mixed strategy Nash equilibrium, and weak dominance. I don't expect you to know any of those things yet, but by the end of chapter one, you'll have those things down. I trust that.

Now, in chapter two, we're going to move on to what we call extensive form games, and this is the opposite of what we were doing earlier, before everyone was making their moves at the same time. Here, the players are taking turns moving. So some examples here are war and invasion plans and police searches. That's getting to what I was talking about before, where I have to decide whether to allow the police officer to search, and then once I have allowed the police officer to do that, then he decides whether to conduct a really thorough search or a really simple search.

So these are times just when we're taking turns moving. And the items we'll cover in this chapter are backward induction, sub-game perfect equilibrium, credible threats, tying hands, commitment problems, and forward induction. Again, I don't expect you to know any of that coming into this, but by the end of chapter two, you will have those things down.

Now, the last chapter, we'll talk about advanced strategic form games. So this is essentially what we covered in chapter one, except we're going to generalize it. So this allows us to ask really important questions like, does a striker kick left more frequently when he's kicking a penalty kick in soccer, as his accuracy to the left side improves? And in this chapter, we'll be talking about comparative statics, which is really the heart and soul of game theory. knife edge equilibria, and symmetric zero-sum games.

Now in terms of practical parts of this course, what are the prerequisites? Well, game theory is logically demanding but rarely requires more than high school algebra. It will help you if you have had a semester's worth of calculus, but even if you haven't, you'll only miss out on what's essentially the last five percent of the course.

So even if you have tiny tiny tiny amounts of math, you'll still be able to do this. Me, personally, I got B's and C's in my high school math classes and now I do this, so... If I'm capable of doing this, I think you're probably capable of doing this, as long as you put in the time and effort to really think about these things.

Now, grading. This is an online class. Let's not take ourselves so seriously.

Congratulations by watching this video and this video only. You've already got an A in the course. Good job. Let's never talk about grades again, because that's ridiculous. Finally, in terms of a textbook, again, this is an online class.

There are no required textbooks because- This is just a made-up thing where you've already gotten an A. But that aside, if you are interested in looking into getting a textbook, this is what I recommend. It's Game Theory 101, the complete textbook.

There's an obvious reason why I'm recommending it to you. It's because I wrote it. But the reason I wrote it is so I could parallel the video series that I'm doing here.

And so what we'll be doing in these lectures actually comes directly out of the book. But the book has many, many, many more examples in every lesson, whereas the video series will just have one per lesson. So it... parallels the video lectures very nicely.

It's also dirt cheap. As I film this, it's $3.99 on Amazon, so that's going to be way cheaper than any other options out there. And then finally, for practical reasons, it's also a teaching book.

If you look at most of the other textbooks on the market, they don't really teach game theory so much as they act as a reference manual for people who already understand these sorts of things, which is really not useful if you're trying to learn game theory. And so one of the reasons I wrote it is to have a teaching book out there that instead of... Assuming that you basically already know game theory treats you like you don't know any game theory at all coming in, and so in the book I go really thoroughly into every step of logic and have all of the mathematical calculations calculated line by line and step by step to really make it as user-friendly as possible.

Now the textbook's also available a la carte, so if you want to buy one chapter each, or I guess one chapter for all three chapters of the video lecture series, you can, although it is significantly more expensive than just buying everything up front. But that's what I recommend, and that actually wraps up what we're going to be talking about today. And in the next video, in the next lecture, we will actually be getting to solving a game, and we're going to start with the Prisoner's Dilemma.

Join me in the next video. Take care.