This is the third in a series about my taking an Open Yale course.

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.