The fourth lecture introduces the notion of Nash Equilibrium. It is basically a way to figure out the best strategy, assuming every player know every other players’ best strategy.

If you know your bast strategy is X, then your opponent will play their best according to your strategy. Knowing what they’ll probably play, you choose the strategy best suited for your opponent’s choice, and they will reciprocate. Lather, rinse, repeat. This happens until a possible equilibrium occurs, where each player agree on a strategy that disadvantages them to stray from. Some games have several Nash Equilibria, and some have none at all.

An example used in class is that of a soccer penalty kick. The keeper knows you’re probably not going to shoot toward the middle of the net, so he chooses a side to dive to. The kicker knows the keeper will probably dive to either side, and the best strategy is to, indeed shot for the opposite side of the dive. It’s self-fulfilling. It’s then just about figuring the odds of a shot in either direction.

In the fifth lecture, Nash Equilibrium is expanded upon to introduce real situations needing coordination. An game is played in class:

You can invest $10 or choose not to. If you do, and 90% of the class does as well, you all gain 5$. If less than 90% of the class invests, you lose the 10$.

Coordination is needed for the “better” common outcome, but may not occur. In this case, most students chose not to invest. We learn that simple communication before the vote does influence the results.

In the sixth lecture, other coordination problems and Cournot Equilibrium is introduced. It could be called the middle ground between perfect competition and monopolies. Collusion is proved to be difficult in certain situations.

More after the 9th lecture.

Essentially, game theory is strategic thinking. It’s also applied math. Is is applied in the fields of business, politics, economics and engineering, to name a few. So far, the professor Benjamin Polak has been great at offering examples that are not only interesting, but engaging.

The professor kicked off the course with a game.

Without showing your neighbor what you are doing, write down on a form either the letter Alpha or the letter Beta. Think of this as a `grade bid’. We will randomly pair your form with one other form. Neither you nor your pair will ever know with whom you were paired. Here is how grades may be assigned for this course.

- If you put Alpha and your pair puts Beta, then you will get grade A, and your pair grade C.
- if both you and your pair put Alpha, then you both will get grade B-.
- if you put Beta and your pair puts Apha, then you will get grade C, and your pair grade A.
- if both you and your pair put Beta, then you will both get grade B+

We learned that Beta is weakly dominated by Alpha in this case.

(here is a link to the pdf of the first lesson)

The first lessons are as such:

1. Never play a strictly dominated strategy
2. Rational play by rational players can still lead to bad outcomes (for example, it’s most rational for both players to play alpha, even though there would be a better outcome if they both played beta)
3. Determine what it is you want, so that payoffs can be accurately measured
4. Put yourself in your opponent’s shoes

The second lecture provided insight into how games are played when repeated, and emphasized putting oneself into our opponents’ shoes. In the third lecture, the median voter theorem was presented in the form of a game,  along with a new set of tools to rationalize decisions in game strategy.

I’m now beginning work on the first problem set.

I’ve read quite a bit about starting a business in the past three years, and I feel I know what I need to know. This couldn’t have happened sooner.

Here’s the first lecture: