*This review is by Zach Smith. A science teacher away from home, enjoying the opportunity to continue learning after university.*

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At the bottom of the screen a timer ticked down, silently judging me. I checked all my answers for a second time, took a deep breath and submitted the final exam. The Coursera loading symbol appeared, and I held my breath, waiting for my results to come up. Ten seconds passed and the tension was thick. Then twenty seconds, then a minute. Five minutes later, I realized that there had been a bug, and refreshed the page, feeling thoroughly embarrassed with myself.

## BACKGROUND

In the past few months I’ve done about a dozen MOOCs, and of all of them, Coursera’s Game Theory II course was the one that I’ve felt most invested in. Maybe it’s because I’m a mathematician at heart, or perhaps it’s that the content is extremely interesting. Either way, my biggest issue without a doubt with the course was that it was only four weeks long. It has a recommended prerequisite of Coursera’s earlier Game Theory course. While I didn’t take this course, it certainly seemed like it would have been a good idea. A little bit of googling on the side caught me up with the most important parts, but the discussion boards in the first couple of weeks suggested that many people were struggling for similar reasons.

## GAME THEORY

The first problem tackled in the course is a discussion of how to create a fair voting system – and in fact, proving that such a thing is impossible for a given definition of ‘fair’.

Game Theory is a field of mathematics that looks at constructions called games. These include, but are not limited to, the things we’d traditionally call a game. Noughts and Crosses is a game, as are Chess and Go. But this course focuses on things that we might not automatically assume. For example, the first problem tackled in the course is a discussion of how to create a fair voting system – and in fact, proving that such a thing is impossible for a given definition of ‘fair’. The rest of the course looks at the broad topic of how to decide the fair prices for things, and how we can encourage people taking part in these exchanges to behave in an honest way.

## THE COURSE

The lectures themselves are excellently delivered – not only are the lecturers clearly very skilled at presentation but they make good use of the tools available to them

The course is very much real mathematics. We begin with an idea of what we’d like to show. Then, over the course of about 80 minutes of lectures, precise definitions are introduced. These definitions are then used to prove some interesting results. If you’re not familiar with the notion of a mathematical proof this might be a bit confusing at first, but if you can appreciate them some of the proofs displayed are extremely elegant. The lectures themselves are excellently delivered – not only are the lecturers clearly very skilled at presentation but they make good use of the tools available to them. Their passion for the topic also shines through when they present, which I think is extremely important.

## QUIZZES & TESTS

There are optional mini-quizzes after each lecture, like most of the courses on Coursera. Grading is done in the form of weekly multiple choice tests, and a timed final exam at the very end. The quizzes follow the standard pattern of a university math course: you’re given a somewhat pathological example of a voting system or a way of pricing goods, say, and have to decide if it meets some of the definitions given in the lectures. It’s one of the things that really tests your ability to apply the ideas directly. The lecturers don’t really give many examples of them solving problems of this variety during the lectures, which could be a problem for some people, but I also think it provides a welcome challenge. Unfortunately the testing is sometimes a little constrained by the format: with a multiple choice question it can sometimes be very easy to guess the answer in a situation even if you couldn’t figure it out for yourself. In this run of the course, we only had two attempts at each quiz (in total), which somewhat offset this.

## SUCCESS

One thing I appreciate is that the scheduling is generous. Although you have to complete one problem set each week, there’s an extra week or so of leeway. This seems to be a more common trend recently and I think it’s a great thing. It means that you can join the course late (like I did) without having missed important deadlines, and that if you’re having a particularly good week you can push yourself through more. The course, while very challenging, is also not very time consuming: I comfortably made it through some of the weeks on two hours of work, whilst still feeling that I learned a lot from it. The forums were filled with people pushing the course to its limit and making sure they learned all the minor details, which while excellent was far from necessary to succeed on the tests. Sadly the staff were not as active on the board as I would have liked – while the material is fabulous it feels like they prepared it and then let it loose on the world without doing too much follow up.

## CONCLUSION

I’d certainly recommend this course to anyone who has a rudimentary understanding of mathematics, and I will be eagerly awaiting a new run of Game Theory I, taught by the same lecturers (and much longer!). But it does come with some pretty heavy downsides: the required expertise, the occasional awkwardness of the testing format and the somewhat unstaffed forums.

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