## Game Theory Course

This idea has been lingering in my mind since the beginning of this semester. During the last holiday (January) I watched a lot about Game Theory course in online videos from Yale University. They provided the videos freely at youtube. If you want to watch it there, you can watch it here

I strongly suggest to watch it directly on youtube for larger view or you can download it and watch on your video player. I did the latter in order to get the best audio of it.

There are totally 24 videos you can watch with each video having 1 hour duration. I haven’t watched all of them, and I also skipped about 3 videos, but I think it’s better to blog it here. The reason is because I find out that this course is really useful whatever major you come from. It’s quiet fun and will make your life brighter in decision making.

All contents of the course belong to Yale University (I’m not Yale’s student, I’m just someone who watched the course from Open Yale Course program) and you can check it at http://oyc.yale.edu/economics/econ-159. The lecturer of this course is Ben Polak (picture shown below) who is an expert on decision theory, game theory and economic history. I don’t know him personally but I think his style of teaching is very understandable.

The content of the video that I’m about to provide is really what I perceive from watching this video. I will try to be as objective as possible in delivering the material. Should any of you come from Yale and took this course (or perhaps participated on the videos), feel free to give any correction if you find any.

So let’s start the journey. The first question that may ring in your mind is “**what is game theory?**” Well, Ben said that game theory is * a method of studying strategic situation*. So what is strategic situation? Ben mentioned the example of non-strategic situation of economy (this course is taught at Economic major but it’s applicable in many parts of our life) about perfect competition in which firms (companies) don’t have to worry about what their competitors doing. Monopoly also an example of non-strategic situation because monopolist doesn’t have any competitor to worry about. But when we have imperfect competition that means we have strategic situation in which the decision taken by a particular company depends on what its competitors do or might do. A good example is Ford must be worried of what GM is doing and what Toyota is doing. Indeed many businesses in the world are in the form of strategic situation. So to put it on more general meaning, strategic means a setting where the outcomes that affect you depend not only on your action alone but also on action of others.

Now, having the meaning in mind, it’s better if I provide a game that Ben used in the video. It is called grade game. There are 2 players – you and your pair in which each player have 2 choice of action – α (alpha) and β (beta). There is nothing to worry about these choice – they are just names. Here is the matrix of the game:

For each choice you and your pair make, there is payoff that you get. This payoff is represented in grades (A,B+,B-,C). In order to make it more comparable, we need to convert it into numbers:

This now a new matrix. It’s really similar to the previous one in which B- is converted to 0, B+ to 1, A to 3 and C to -1. Ben said that these numbers are utilities that each player try to maximize (their goals). Moreover, assume the players are people who only care about their own grade (they concern only on their grade) – Ben called these type of people “Evil gits”. LOL. Now if you have to choose (indeed you shall choose in the game), which option will you take? α or β? Our common sense will tell us that it’s always better to choose α because no matter what your pair choose, you will always get higher payoff if you choose α. Suppose your pair choose α as well, then you get 0 by choosing α and -1 by choosing β. It’s clear that 0 is a better payoff that -1. The same applies when your pair choose β, you will get 3 by choosing α and 1 by choosing β. Again, 3 is better than 1. This case tell us that α dominates β (β is a “strictly dominated strategy”). So lesson number 1 in game theory is “*Do not play a strictly dominated strategy*“. The obvious reason is you will always have better payoff by playing a strategy that dominates it.

Now the second lesson of game theory is “Rational choice can lead to outcomes that suck”. This is a famous Prisoner’s Dilemma. You probably have heard this term before. You can read about it in more detail from other sources but here is the brief story. There were 2 accused criminals who were being interviewed separately by police. They were told to rat each other out. If none of them rat the other guy out, they are being jailed for 1 year. If both of them rat each other out, both are jailed 2 years. But if you rat the other guy out, and he doesn’t rat you out then you will go home free and that other guy will be jailed 5 years. So according to Prisoner’s Dilemma both of them will be better off by choosing “confess” or rat each other out. While according to our previous rule, not confessing is a rational choice you should make to maximize our payoff (remember we’re still ‘Evil gits’). So this example clearly shows that sometimes rational choice can lead to bad outcome.

Moving on to the third lesson. Let’s see the new matrix now.

Suppose now we have a different type of player called “indignant angel”. These type of people who feel guilty for having better payoff than the other player (who is also indignant angel). From the above picture, the payoff of me choosing α and my pair choosing β is -1 for me and -3 for her. The reason why I (as indignant angel) get -1 is because while I get A grade (which is converted to 3) I also feel guilty for making my pair get lower payoff. So we subtract 4 (the magnitude of my guilt) from 3 (the benefit I get for having A grade). So this is a kind form of morality. Moreover, the reason I get -3 when I choose β and my pair choose α is because I feel worried how to explain this C grade to my parents (-1 in magnitude) while I also feel indignant against my pair because she made me got a ‘C’. So consider this additional indignant takes us down -2. Combined these give use -3 in total in the case.

Given these illustration we can see that we no longer have any dominant strategy. If my pair choose α, then my choosing α will be better (0 is better than -3). But if she choose β, I will rather choose β also (1 is better than -1). So there is no dominant strategy and of course no “strictly dominated strategy”. This game is called “coordination game” and will be explain in great detail in next videos. But the crux of this game is “payoff matters”. You change the payoffs, you’ll get different game (indignant angel vs indignant angel) with different outcome.

Now let’s try to analyze the last type of game. Suppose you’re an evil git and your pair is an indignant angel. The payoff matrix will be like:

Actually, you (as the evil git – who only care about your own payoff) will again choose α because it is a dominant strategy here. However what if we flip it now. You are the indignant angel and your pair is the evil git. Here the matrix payoff looks like.

Here,, as an indignant angel you also don’t have any dominant strategy as the case of indignant angel vs indignant angel before. α is better against α, and β is better against β. But if you look from your pair’s perspective, you will figure out that her α dominates her β. She will choose α regardless of your choice in order to maximize her payoff (she is an evil git anyway). So, knowing that she will choose α, it’s better for you to choose α (because for you α is better against α). This is the lesson called “Put yourself into others’ shoes and try to figure out what they will do”.

So these are the 4 basic lessons of Game theory from this lecture. Actually there is the 5th one, but I don’t want to mention it here. You should watch the full video to figure it out. However, at last, these 4 lessons are not sufficient to show you the fun part of game theory. There are other 23 videos that you really should watch and learn. There are plenty of stuffs you will discover such as Nash equilibrium, backward induction, and real life examples from economy, sports, politics, etc. I personally enjoy this course greatly and I hope you will get the same (or better) enjoyment from learning this course.

Note: All the pictures I showed above are taken from the lecture note of the video.

tidaIf everybody is not playing a strictly dominated strategy, does that mean nobody is getting anything? Or what do the numbers actually imply?

Starting from the prisoner’s dilemma, it is getting confusing (or is it just because it is getting pretty late and my brain has stopped working halfway?). Whatever the reason is, several paragraphs later, I was like… “dafuq?!”

So, in brief, how should I apply this to my daily decision making? haha Or in the end everything is paradox?

March 9, 2012 at 12:51 am

darwinxieWell if all players don’t play strictly dominated strategy (in this case beta), then they will choose alpha (if both of them are evil git who only care about their own payoff).

The numbers actually represent the payoff you will get by playing that particular strategy. It’s like the benefit you want to achieve. All players of course will try to get maximum payoff as possible.

The applications are mostly mentioned in the remaining 23 videos. About the paradox, it’s something related to “who know first”, something called as sequential game. Again all of the details are presented in the remaining videos. So you should watch them if you want. But it will take long time though.

Thanks for landing on this blog…

March 9, 2012 at 11:01 am