- Assume the frequency dependent selection model for a population with two types of individuals: $x=(x_1, x_2)$ such that $x_1 + x_2 = 1$. Obtain all the stable distribution for the sytem defined by the following fitness functions:
- $f_1(x)=x_1 - x_2\qquad f_2(x)=x_2 - 2 x_1$
- $f_1(x)=x_1x_2 - x_2\qquad f_2(x)=x_2 - x_1 + 1/2$
- $f_1(x)=x_1 ^ 2 \qquad f_2(x)=x_2^2$

- For the following games, obtain all the stable distributions for the evolutionary game:
- $A = \begin{pmatrix}2 & 4 \\ 5 & 3\end{pmatrix}$
- $A = \begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$

- Define:
- mutated population.
- Evolutionary stable strategies

- State and prove the general condition for ESS theorem.
- Using the general condition for ESS theorem identify what strategies are evolutionarily stable for the games of question 2.

Source code: @drvinceknight Powered by: Python Mathjax Github pages Skeleton css