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“The British have little sense of pavement etiquette, preferring a slalom approach to pedestrian progress. When two strangers approach each other, it often results in the performance of a little gavotte as they double-guess in which direction the other will turn.”

“Telling people how to walk is simply not British.”

“But on the street? No, we donâ€™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
```

```
# Let us plot a large number of these interactions
num_of_walks = 500
num_of_reps = 2000
bins = 20
plt.hist([walk(num_of_walks) for k in range(num_of_reps)], bins=bins);
```

```
# What if everyone walks on the left?
def walk(number_of_walks):
"""
Simulate people walking along the pavement
"""
reds = [random.choice('L') for k in range(number_of_walks)]
blues = [random.choice('L') for k in range(number_of_walks)]
bumps = sum([reds[k] != blues[k] for k in range(number_of_walks)])
return bumps
plt.hist([walk(num_of_walks) for k in range(num_of_reps)], bins=bins);
```

```
# What if 1 person walks on the left and the other on the right?
def walk(number_of_walks):
"""
Simulate people walking along the pavement
"""
reds = [random.choice('L') for k in range(number_of_walks)]
blues = [random.choice('R') for k in range(number_of_walks)]
bumps = sum([reds[k] != blues[k] for k in range(number_of_walks)])
return bumps
plt.hist([walk(num_of_walks) for k in range(num_of_reps)], bins=bins);
```

```
# 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]))
plt.plot(red_data);
plt.plot(blue_data);
```

Mathematics can help understand how behaviour emerges.

TV show from Feb 2008 to Feb 2009 where a jackpot is to be shared between 2 contestants who secretly choose to "split" or "steal".

- If both players "split", the jackpot is split equally between them.
- If 1 player "splits" and the other "steals", the stealer gets the whole jackpot and the splitter leaves with nothing.
- If both players "steal", they both leave with nothing.

Cooperate | Defect | |

Cooperate | (3,3) | (0,5) |

Defect | (5,0) | (1,1) |

Always cooperate.

Always defect.

Start by cooperating and then switch.

Play randomly.

Start by cooperating and then do whatever your opponent does in the previous round.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |

Alternator | C | D | C | D | C | D | C | D |

Tit For Tat | C | C | D | C | D | C | D | C |

C | D | |

C | (3,3) | (0,5) |

D | (5,0) | (1,1) |

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |

Alternator | 3 | 5 | 0 | 5 | 0 | 5 | 0 | 5 |

Tit For Tat | 3 | 0 | 5 | 0 | 5 | 0 | 5 | 0 |

Alternator | Cooperator | Defector | Random | Tit For Tat | |

Alternator | 2.0 | 4.0 | 0.5 | 2.3 | 2.5 |

Cooperator | 1.5 | 3.0 | 0.0 | 1.5 | 3.0 |

Defector | 3.0 | 5.0 | 1.0 | 3.0 | 1.0 |

Random | 2.2 | 4.0 | 0.5 | 2.3 | 2.7 |

Tit For Tat | 2.5 | 3.0 | 1.0 | 2.3 | 3.0 |

- Economics
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(1928-2015)