Introducing strategies with matching penniEs

Today we mainly talked about what a strategy was: defining it as a way of picking actions.

A recording of this class is available here: https://cardiff.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=3a87cbb9-72fa-4a03-a335-b10500c67c26

We did this by pairing up and playing two different games:

1. The traditional matching pennies game defined by the two payoff matrices: \(A=\begin{pmatrix}1 & -1\\-1 & 1\end{pmatrix}\) and \(A=-B\).
2. The modification of matching pennies which is the game defined by the two payoff matrices: \(A=\begin{pmatrix}2 & -2\\-1 & 1\end{pmatrix}\) and \(A=-B\).

As well as briefly talking about strategies we mainly made sure everyone understood the notion of picking from an action set, how this is not necessarily random but also what we would mean by random.

I briefly (because I’m an idiot and thought I had 10 less minutes than I did): showed how to define a game using nashpy. If you would like to download the notebook I wrote in class it is here.

At the end of class someone came up to me and said that for the second game, they actually both chose their actions for the entire 5 plays before showing them (as opposed to picking, showing and then picking the next). This is arguably a “right way to do it” as the strategy is completely independent of the actions of the opponent.