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Introduction to Game Theory

This post gives an introduction to the fascinating topic of Game Theory and describes what to expect in the upcoming course on this- starting Aug 29, 2020. Click here to know more about Navin and register for the upcoming course.

By Christopher X Jon Jensen (CXJJensen) & Greg Riestenberg - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=19680869

Play, Motivation and Learning

Playing games is usually not associated with learning and education. Parents are more likely to view games as a waste of time rather than as something that can impart life-long skills. In fact, students also agree with this assessment, the only difference being that the students actually don't mind the waste of time as much.

So it is not a surprise that the most common student feedback I receive for the Game Theory course I teach is "I enjoyed playing various games and this course was extremely good!!" or "There could be more games" or "I would increase the number of games played per class" or "The course could be 2 hours instead of 1. That way we could play more games."

However, before you jump to conclusions, let us look at what is happening while the students are playing the games. One student said: "I did not expect it to be this informative." Or "I have learnt and evolved from what i was a week ago," or "I learnt so much in the past few days and i could finally spend some part of quarantine productively," and "The thing I liked most about the course was learning about payoff matrixes."

Ok. So it is not all fun and games. There are matrices. And, as the course title implies, there is theory to be studied. And every day, I would give homework that did not involve any game playing, but rather required understanding and applying the theory learnt

in class.

What did students have to say about the homework? "The homework was nice and overall I learned a lot." And: "If I could make one change to the course, I would try to bring in more homework." And best of all: "The one thing I liked about the course was the homework. It really made me think and understand each concept better so it was something I liked a lot, even if I don't usually like homework."

One child even said: "The homework sometimes was a bit less." (We're sorry! We'll fix this right away . If students are asking for more homework, we are definitely not going to say no!)

What is Game Theory and what happens in this Course?

So what do we do in this course? We start with simple games, which are easy to understand and easy to analyse, and then understand the different strategies that could be used to play/win the game.

For example, consider this video clip from the movie Footloose:

The Game of Chicken shown in this video clip has been extensively studied by economists and helps determine strategies in fields as diverse and important as terrorist negotiations, workers' strikes, and nuclear weapons deterrents.

This is the Game of Chicken. Try to think of what you would do, or not do, if forced to play this game. There aren't too many possibilities or strategies. And yet, as you can see from the Wikipedia page for the Game of Chicken ,there is lots of theory related to it, and it comes up in many different real life situations, and the strategies you learn in the simple version of this game can actually be applied in more complex real life situations.

For example, have you heard the phrase, "America does not negotiate with terrorists"? This is directly connected to the theory of the Game of Chicken, and the video you saw above (and the steering wheel which got stuck.)

There are more games and more real life scenarios that become easy to understand once seen from the point of view of Game Theory.

Should two students in the same class share class notes and study tips with each other, or should they keep them secret from each other? Should you trust your cook with the house keys, or not?

When two companies are selling complementary products to the same set of customers, should they collaborate with each other, or should they compete by introducing products in the others' space?

In case of the students, if both students share notes and tips with each other the performance of both will improve. But if you share sincerely, while the other person only pretends to share, never sharing the important or useful stuff, then they will benefit but you will lose out. What should you do?

For the cook, if you give her the house keys, there is a risk that she'll steal something. If you don't give her the house keys, then you always have to be around when it is time for her to come and cook, so it significantly reduces your flexibility, and increases your overhead. Game theory analysis gives guidance on when you can trust the cook, and when you shouldn't, which sometimes goes against our instincts.

Questions like these come up all the time in life, in work as well as in personal relationships. Most people take such decisions intuitively, but there isn't necessarily a deep thought process behind the decision, and often the decisions are suboptimal.

Economists and mathematicians have been studying situations like these for a long time, and have developed a science of decision-making (called game theory) where these are modeled as simple games that are easy to analyze, but at the same time give deep insights into how you can significantly improve on your instinct in actual messy real-life situations. 12 economists have won 7 Nobel Memorial Economics prizes in Game Theory (including John Nash, whose story is shown in the movie A Beautiful Mind).

The examples in the first paragraph are all instances of one particular game (called Iterated Prisoners' Dilemma).

In this class the students play 3 or 4 different such games against each other, then discuss and compare their strategies/techniques with those of the other students, followed by a discussion of the theory of that game, variations and complexities, and a discussion of possible real-life scenarios where those theories are applicable. This is followed by homework where the concepts learnt have to be applied to new real-life situations.

Spreadsheets tabulated in the course to analyse and evaluate strategies

And the best part is that all this involves little or no math. In fact, most of it doesn't look anything like studies, since it primarily involves playing games and thinking about games! If this excites you, I look forward to interacting with you in the next edition of my course!