Replicator Dynamics

Notes

• https://nashpy.readthedocs.io/en/stable/text-book/replicator-dynamics.html

Videos

1. Evolution of aggression and sharing: the replicator dynamics with the Hawk Dove Game - YouTube - Private

2. A mathematical model of evolution: the replicator dynamics equations. - YouTube - Private

3. Stability of the replicator dynamics equation. - YouTube - Private

4. Evolutionary stability of the Replicator Dynamics Equations - YouTube - Private

5. Allowing for mutation in evolution: the replicator mutation dynamics equations. - YouTube - Private

6. Using Python to solve the Replicator Dynamics Equation with Nashpy - YouTube - Private

Class meeting notes

• https://github.com/drvinceknight/gt/blob/main/do/07-evolutionary-game-theory.rst

Typical Programming Exercises

1. Create a variable populations which has value a list containing all population vectors for the replicator dynamics (with timepoints=numpy.linspace(0, 1, 500)) for the Normal Form Game defined by: \(A = \begin{pmatrix}1 & - 1\\ -1 & 1\end{pmatrix} \qquad B = \begin{pmatrix}-1 & 1\\ 1 & -1\end{pmatrix}\)
2. Output a list containing all population vectors for the replicator dynamics (with timepoints=numpy.linspace(0, 1, 500)) for the Normal Form Game defined by: \(A = \begin{pmatrix}3 & 2\\ 3 & 1\end{pmatrix} \qquad B = \begin{pmatrix}4 & 9\\ 5 & 3\end{pmatrix}\)
3. Create a variable last_population which has value the final population vectors for the replicator dynamics (with timepoints=numpy.linspace(0, 1, 500)) for the Normal Form Game defined by: \(A = \begin{pmatrix}1 & - 1\\ -1 & 1\end{pmatrix}\)
4. Output the final population vectors for the replicator dynamics (with timepoints=numpy.linspace(0, 1, 500)) for the Normal Form Game defined by: \(A = \begin{pmatrix}-3 & - 1 & 4\\ 2 & -1 & 1\\ 0 & 3 & -2\end{pmatrix}\)

Solutions

Log of past relevant classes

02/23/24: Replicator dynamics

In class we spoke about the replicator dynamics equation: a differential equation that is a building block of evolutionary game theory.

04/24/23: A paper on applying Game Theory to cancer

In class today I discussed this paper: Studying the emergence of invasiveness in tumours using game theory.

03/07/23: Ambulance diversion and replicator dynamics

In class today Michalis Panayides presented research from his PhD. Michalis’ work uses queuing theory to build a Normal Form Game between two hospitals. This is used to identify a good set of incentives/targets to help reduce ambulances being blocked outside of Accident and Emergency departments.