Duration: 25 minutes

Objectives¶

• Compute the probability of fixation in the Hawk Dove game using the formula.

Notes¶

For:

$\begin{split}A = \begin{pmatrix} 0 & 3\\ 1 & 2 \end{pmatrix}\end{split}$

Ask students to work in pairs, using the formula to compute $$x_1$$.

This is given by:

\begin{split}\begin{align} f_{1i} &= \frac{3(N-i)}{N - 1}=3\frac{N-i}{N-1}\\ f_{2i} &= \frac{i+2(N - i -1)}{N - 1}=\frac{2N-2-i}{N - 1}\\ \end{align}\end{split}

This gives (for $$N=4$$):

$$i=1$$ $$i=2$$ $$i=3$$
$$f_{1i}$$ 3 2 1
$$f_{2i}$$ 5/3 4/3 1
$$\gamma_i$$ 5/9 2/3 1

Thus:

$x_1 = \frac{1}{1 + 5/9 + 5/9\times2/3 +5/9\times2/3\times1}=\frac{1}{62/27}=\frac{27}{62}\approx.44$