Category Archives: Game Theory

Your chance to get to know Game Theory!

Good evening,

There is a section in this blog that I haven’t been able to fill with new content for a long time: the part dedicated to Game Theory. The main reason is that I’m not using that field in my day-to-day job, so it’s a bit difficult to find good and accessible topics to discuss here.

However, I have good news for those of you who are eager to discover more about this topic. A few months ago, I told you about Coursera in this post. For those of you who missed it, Coursera provides users with free high quality online classes from top-tier universities.

By now, you probably guessed what this post is all about! As a matter of fact, starting January 7th 2013, there will be a Game Theory from Stanford University available to us. You can check out all the details and register for the class on the official page. Here is the abstract of the class:

Popularized by movies such as “A Beautiful Mind”, game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Beyond what we call ‘games’ in common language, such as chess, poker, soccer, etc., it includes the modeling of conflict among nations, political campaigns, competition among firms, and trading behavior in markets such as the NYSE. How could you begin to model eBay, Google keyword auctions, and peer to peer file-sharing networks, without accounting for the incentives of the people using them? The course will provide the basics: representing games and strategies, the extensive form (which computer scientists call game trees), Bayesian games (modeling things like auctions), repeated and stochastic games, and more. We’ll include a variety of examples including classic games and a few applications.

For those of you who haven’t seen the movie “A beautiful mind” yet, I strongly encourage you to do it, and if you’re not yet convinced, here is the trailer:

[youtube:http://www.youtube.com/watch?v=Q3G9lnyXJGU&rel=0]

About the class itself, the description says it is based on a book I extensively used for my paper on Penalty Shots in Ice Hockey, and which is available on Amazon:

Essentials of Game Theory: A Concise, Multidisciplinary Introduction (Synthesis Lectures on Artificial Intelligence and Machine Learning)

Both authos, Kevin Leyton-Brown and Yoav Shoham are two leading contributors of the game theory field and they are both professors of the class. Hence, I can’t emphasize enough how good I think this class will be.

I do not expect I will be available to take all the exercises because my spare time will be mainly dedicated to the CFA Level II (see the countdown at the top of the menu on the right), but if you wish to do so, don’t forget you can get a certificate of completion.

That’s it for now! Please let me know what you think of the class!

See you next time!

Penalty Shots in Ice Hockey: a game-theoretic approach.

Good afternoon everybody,

As I promised a few days ago, I am now uploading the first research I made regarding game theory applications to Sports.

As you have probably guessed by now, the aim of this project was to model the penalty shot situation in Ice Hockey, and to find the equilibrium.

This research was made in collaboration with Geneva Servette Hockey Club (GSHC) and in particular with the help of Sébastien Beaulieu who I would like to thank again for his support.

You can download the file here, and the abstract is provided below:

This paper aims to analyze the penalty shot piece of play in Ice Hockey within a game-theoretic framework. A mathematical model will be provided for this situation in order to apply the Bayesian games setup. To make the model more realistic, measures taken with a professional ice hockey club will be used. The data will then be used to compute the mixed strategies equilibria and the meaning of these results will be discussed.

The results if this study provide a mixed strategy equilibrium with probabilities that could possibly be applied by players.

I think it would be a good idea to see if these strategies are actually being used by professional hockey players, maybe using videos. I would be glad if something conducted such research.

For those of you who do not wish to look at the mathematical aspects of the modeling, you can simply skip part 3 and focus on the introduction and the conclusion.

Please feel free to post comments to let me know your feedback.

See you soon for more.

What about Game Theory?

Hi everybody,

Just a little introductory post about the “Game Theory” section of this blog.

I like to say that game theory is the link between mathematics, economics and human behavior. It is a special field of mathematics aimed to analyze and understand conflicting situations. A comprehensive summary of the field is available on this page, and there is an interesting blog available here.

My aim in this blog is not to talk about the theoretical/purely mathematical aspects of Game Theory, but more to apply the concept to real world situations. As a matter of fact, there are a lot of classic, day to day situations where this field can be applied, and I would like to analyze a few of those and provide intuitive solutions. I am particularly interested in applications concerning the sports world.

I will soon post a research I made during my studies at the EPFL, in the Computational Game Theory class. The idea what to discuss a game-theoretic approach to penalty shots in Ice Hockey.

Until then, have a nice evening!