# Strategies

### Notes

### Videos

Choosing actions in Game Theory: Strategies for Rock Paper Scissors - YouTube - Private

Definition of a strategy in Game Theory - YouTube - Private

Definition of the support of a strategy: what actions will be played - YouTube - Private

Calculating expected utilities when strategies interact in Game Theory - YouTube - Private

A linear algebraic approach to computing expected utilities in Game Theory - YouTube - [Private] - A linear algebraic approach to computing expected utilities in Game Theory

Using python to calculate expected utilities in Game Theory with Nashpy - YouTube - Private

## Typical Programming Exercises

- Create a variable
`utilities`

which has value the expected utilities for both players for the following Normal Form Game when the row player is playing \(\sigma_r=(.4, .6)\) and the column player is playing \(\sigma_c=(0, 1)\):
\(A = \begin{pmatrix}1 & - 1\\ -1 & 1\end{pmatrix} \qquad B = \begin{pmatrix}-1 & 1\\ 1 & -1\end{pmatrix}\)
- Output the expected utility for both players for the following Normal Form Game when the row player is playing \(\sigma_r=(1 / 3, 2 / 3)\) and the column player is playing \(\sigma_c=(1 / 2, 1 / 2)\):
\(A = \begin{pmatrix}3 & 2\\ 3 & 1\end{pmatrix} \qquad B = \begin{pmatrix}4 & 9\\ 5 & 3\end{pmatrix}\)
- Create a variable
`utilities`

which has value the expected utilities for both
players for the following zero sum Normal Form Game
defined by:
\(A = \begin{pmatrix}1 & - 1\\ -1 & 1\end{pmatrix}\)
when the row player is playing \(\sigma_r=(0, 1)\) and the column player is
playing \(\sigma_c=(1/4, 3/4)\).
- Output the expected utilities for both players for the following zero sum Normal Form Game
defined by:
\(A = \begin{pmatrix}-3 & - 1 & 4\\ 2 & -1 & 1\\ 0 & 3 & -2\end{pmatrix}\)
when the row player is playing \(\sigma_r=(0, 1, 0)\) and the column player is
playing \(\sigma_c=(1/4, 1/4, 1/2)\).

Solutions

## Log of past relevant classes

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

Today was a fun class: thanks! We spoke about calculating utilities as well as
best responses.

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