Best responses

Notes

• https://nashpy.readthedocs.io/en/stable/text-book/best-responses.html#best-responses

Videos

1. Best way to respond in Game Theory: how to choose what to do when matching pennies. - YouTube - Private

2. The definition of a Best Response in Game Theory - YouTube - Private

3. Best responses in small games: exact calculations for 2 by 2 Normal Form Games. - YouTube - Private

4. A general condition for a strategy to be a best response in Game Theory - YouTube - Private

5. When no player has a reason to change: Nash equilibrium - YouTube - Private

6. Using Python to check if strategies are best responses to each other - YouTube - Private

Class meeting notes

• https://github.com/drvinceknight/gt/blob/main/do/02-best-response-condition.md

Typical Programming Exercises

1. Create a variable are_best_responses which has value a tuple of booleans indicating if the following pairs of strategies are best responses to each other for the Normal Form Game when the row player is playing \(\sigma_r=(.4, .6)\) and the column player is playing \(\sigma_c=(0, 1)\): \(A = \begin{pmatrix}1 & - 1\\ -1 & 1\end{pmatrix} \qquad B = \begin{pmatrix}-1 & 1\\ 1 & -1\end{pmatrix}\)
2. Output a tuple of booleans indicating if the following pairs of strategies are best responses to each other for the Normal Form Game when the row player is playing \(\sigma_r=(1 / 3, 2 / 3)\) and the column player is playing \(\sigma_c=(1 / 2, 1 / 2)\): \(A = \begin{pmatrix}3 & 2\\ 3 & 1\end{pmatrix} \qquad B = \begin{pmatrix}4 & 9\\ 5 & 3\end{pmatrix}\)
3. Create a variable are_best_responses which has value a tuple of booleans indicating if the following pairs of strategies are best responses to each other for the Normal Form Game when the row player is playing \(\sigma_r=(0, 1)\) and the column player is playing \(\sigma_c=(1/4, 3/4)\): \(A = \begin{pmatrix}1 & - 1\\ -1 & 1\end{pmatrix}\)
4. Output a tuple of booleans indicating if the following pairs of strategies are best responses to each other for the zero sum Normal Form Game when the row player is playing \(\sigma_r=(0, 1, 0)\) and the column player is playing \(\sigma_c=(1/4, 1/4, 1/2)\): \(A = \begin{pmatrix}-3 & - 1 & 4\\ 2 & -1 & 1\\ 0 & 3 & -2\end{pmatrix}\)

Solutions

Log of past relevant classes

02/05/24: Best responses against computer strategies

In class today we spoke more about strategies which are methods for picking actions from action sets. Specifically we spoke about best responses: what is the best strategy when faced with a given strategy.

04/25/23: Zero Determinant strategies and CCU interactions

In class today I discussed this paper two papers:

02/14/23: Valentines day

In today’s class we spoke about a deadline for the individual coursework but spent most of our time taking the initial steps that a research project would take to model gift giving for Valentines day.

02/10/23: More best responses

Friday’s class was hopefully helpful: we spent some time working on drawing linear functions for best response calculations.

02/07/23: Utility calculations and the start of best responses

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