### Evolutionary Mathematics [@drvinceknight](https://twitter.com/drvinceknight) {[github.com](https://github.com/Axelrod-Python/Axelrod), [gitter.im](https://gitter.im/Axelrod-Python/Axelrod)}/Axelrod-Python/Axelrod


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Advice for foreigners on how Britons walk

“Telling people how to walk is simply not British.”
“But on the street? No, we don’t walk on the left or the right. We are British and wander where we will..”

import random

def walk(number_of_walks):
    Simulate people walking along the pavement
    reds = [random.choice('LR') for k in range(number_of_walks)]
    blues = [random.choice('LR') for k in range(number_of_walks)]
    bumps = sum([reds[k] != blues[k] for k in range(number_of_walks)])
    return bumps

from bashplotlib.histogram import plot_hist  # cli plots

def plot_experiment(data):
    return plot_hist(data,
                     height=20,  # Set the height
                     colour='red',  # Set the colour
                     bincount=20,  # Number of bins
                     showSummary=True)  # Show a summary

plot_experiment([walk(500) for k in range(1000)])

# Evolutionary dynamics with a mutation rate:
size_of_population = 100  # Number of people
number_of_rounds = 500  # How many rounds
mutation_rate = .05  # Chance of changing strategy
death_rate = .05  # Chance of removal

reds = ['L' for k in range(size_of_population)]
blues = ['L' for k in range(size_of_population)]
red_data = [sum([k == 'L' for k in reds])]
blue_data = [sum([k == 'L' for k in reds])]

for rnd in range(number_of_rounds):  # Loop through rounds
    for j, pair in enumerate(zip(reds, blues)):  # Loop through players

        if random.random() < mutation_rate:  # Check if random change
            reds[j], blues[j] = random.choice('LR'), random.choice('LR')

        if pair[0] != pair[1]:  # If bump
            if random.random() < death_rate:  # If mind change
                reds[j], blues[j] =  blues[j], reds[j]

    red_data.append(sum([k == 'L' for k in reds]))  # Data collection
    blue_data.append(sum([k == 'L' for k in blues]))

Prisoner's Dilemma

$$\begin{pmatrix} 3,3&0,5\\ 5,0&1,1 \end{pmatrix}$$
  1. Robert Axelrod
  2. 1980a: 14+1 strategies
  3. 1980b: 64+1 strategies

TODO: Sacrifice a cat

class TitForTat(Player):
    """A player starts by cooperating and then mimics previous move by opponent."""

    name = 'Tit For Tat'
    classifier = {
        'memory_depth': 1,  # Four-Vector = (1.,0.,1.,0.)
        'stochastic': False,
        'inspects_source': False,
        'manipulates_source': False,
        'manipulates_state': False

    def strategy(opponent):
        return 'D' if opponent.history[-1:] == ['D'] else 'C'

class TestTitForTat(TestPlayer):

    name = "Tit For Tat"
    player = axelrod.TitForTat
    expected_classifier = {
        'memory_depth': 1,
        'stochastic': False,
        'inspects_source': False,
        'manipulates_source': False,
        'manipulates_state': False

    def test_strategy(self):
        """Starts by cooperating."""

    def test_effect_of_strategy(self):
        """Repeats last action of opponent history."""
        self.markov_test([C, D, C, D])
        self.responses_test([C] * 4, [C, C, C, C], [C])
        self.responses_test([C] * 5, [C, C, C, C, D], [D])

class MindBender(MindWarper):
    A player that changes the opponent's strategy by modifying the internal

    name = 'Mind Bender'
    classifier = {
        'memory_depth': -10,
        'stochastic': False,
        'inspects_source': False,
        'manipulates_source': True,  # changes what opponent will do
        'manipulates_state': False

    def strategy(opponent):
        opponent.__dict__['strategy'] = lambda opponent: 'C'
        return 'D'


`pip install axelrod` {[github.com](https://github.com/Axelrod-Python/Axelrod), [gitter.im](https://gitter.im/Axelrod-Python/Axelrod)}/Axelrod-Python/Axelrod [Blog posts by TC](http://www.thomascampbell.me.uk/category/axelrod.html) [demo.ipynb](https://github.com/drvinceknight/Talks/blob/gh-pages/2015-10-12-Evolutionary-mathematics/demo.ipynb)