In class today we looked at the Moran Process. We did this by considering the Hawk Dove game.
You can see a recording of this here.
The Moran process is a game theoretic model of evolution. One of the differences from the Replicator Dynamics equation is that the population is assumed to be finite: so we assumed there is a finite population of \(N\) individuals that can be of any of the types that correspond to actions of the underlying Norma Form Game.
In the example of the Hawk Dove game that we played in class we assumed there were \(N=3\) individuals and the question we attempted to understand was: if we introduce a Hawk in to a population of Doves, what will happen?
The Moran process then follows the following:
Repeat that process until there is a single type of individual in the population.
In class we used dice to simulate the above and obtained a probability of 48% of the Hawk taking over.
Here is a notebook with some numeric simulations of the probabilities. If you look through the notes you can see approaches for calculating exact fixation probabilities.
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