Modelling and Simulating Social Systems
with MATLAB
Lesson 4 – Introduction to Agent-based simulations
A. Johansson & W. Yu
© ETH Zürich |
Datum
Lesson 4 - Contents
 Swarm intelligence
 Human cooperation and coordination
 How to develop a multi-agent simulator
 Exercises
2008-03-09
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Swarm Intelligence
 Decentralization
 Interaction
 Self-organization
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Boids (Reynolds,1986)
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More information: http://www.red3d.com/cwr/boids/
Separation: steer to
avoid crowding local
flockmates
Alignment: steer
towards the average
heading of local
flockmates
Cohesion: steer to move
toward the average
position of local
flockmates
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Human Cooperation
 Prisoner’s dilemma
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15,15
20,0
0,20
19,19
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The Evolution of Cooperation (Axelrod,1984)
 Tit for tat
 Shadow of the future
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Coordination
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1,1
0,0
0,0
1,1
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Learning
 Imitation
 Reinforcement
 Best reply
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From Factors to Actors (Macy,2002)
 Agents are autonomous
 Agents are interdependent
 Agents follow simple rules
 Agents are adaptive and backward-looking
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Programming a simulator
 Agent based simulations

The models simulate the simultaneous operations of
multiple agents, in an attempt to re-create and predict
the actions of complex phenomena.

Agents can be pedestrians, animals, customers,
internet users, etc…
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Programming a simulator
 Agent based simulations
State update
According to set of
behavioral rules
Time t
Time t + dt
Characterized by a state
(or states)
New state
(location, dead/alive,
color, level of excitation)
Time line
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T1
dt
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T2
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Programming a simulator
 Agent based simulations
State update
According to set of
behavioral rules,
including neighborhood
Time t
Time t + dt
Characterized by a state
New state
(location, dead/alive,
level of excitation)
Time line
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T2
T1
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Programming a simulator
 Programming an agent based simulator often
goes in five steps

Initialization
Initialization
- Initial state; parameters; environment

Time loop
Time loop
Agents loop
- Processing each time steps

Agents loop
Update state
- Processing each agents

end
Update
end
- Updating agent i at time t

Save data
Save data
- For further analysis
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Programming a simulator
 Step 1: Defining the initial state & parameters
% Initial state
t0=0;
dt=1 ;
T=100;
%begining of the time line
%time step
%number of time steps
%Initial state of the agents
State1 = [0 0 0 0];
State2 = [1 1 1 1];
etc…
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Programming a simulator
 Step 1: Defining the initial state & parameters
% Initial state
t0=0;
dt=1 ;
T=100;
%begining of the time line
%time step
%number of time steps
%Initial state of the agents
State1 = zeros(1,50);
State2 = rand(1,50);
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Programming a simulator
 Step 2: Covering each time step
% time loop
For t=t0:dt:T
What happen at each time step?
- Update environment
- Update agents
end
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Programming a simulator
 Step 3: Covering each agent
% agent loop
For i=1:length(States)
What happen for each agent?
end
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Programming a simulator
 Step 4: Updating agent i at time t
% update
% Each agent has 60% chance to switch to state 1
randomValue=rand();
if (randomValue<0.6)
State(i)=1;
else
State(i)=0;
end
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Use sub-functions for
better organization!!
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Programming a simulator
 Step 4: Updating agent i at time t
% update
% Each agent has ‘proba’ chance to switch to state 1
randomValue=rand();
if (randomValue<proba)
State(i)=1;
else
State(i)=0;
end
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Define parameters in
the first part!!
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Programming a simulator
 Step 4: Updating agent i at time t
% Initial state
t0=0;
dt=1 ;
T=100;
proba=0.6;
2008-03-09
%begining of the time line
%time step
%number of time steps
%probability to switch state
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Define parameters in
the first part!!
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Programming a simulator
 Step 5: Final processing
% Outputs and final processing
propAlive = sum(states)/length(states);
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And return propAlive
as the output of the
simulation.
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Programming a simulator
 Running simulation
>> p=simulation()
p =
0.54
>> p=simulation()
p =
0.72
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Programming a simulator
 Alternatively : a framework for the simulator
% Running N simulations
N=1000
%number of simulation
for n=1:N
p(n)=simulation();
end
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Use a framework to
run N successive
simulation and store
the result each time.
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Programming a simulator
 Alternatively : a framework for the simulator
>> hist(p)
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A simple dice game
 The rules:
Each player throws 2 dice and gain a number of points equal to the
sum of the two dice. If the dice produce the same value, the score is
double.
2;5
:7
Normal score
4;4
: 8 x 2 = 16
Bonus score
The players roll the dice N times, in turn. Each one cumulate his
points. The player that has the best score after N rolls win.
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A simple dice game
 The cheater:

There is a cheater among the players. This cheater own some special
dice that have a higher probability to produce the same value.
In a multi-agents simulation, each player would be an agent
characterized by his score, and his behaviour (cheater or fair
player).
We now develop this simulation…
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Exercise 1
 The behaviour of a fair player:

Write a function called fairRoll.m that returns the score of a fair player:
- Inputs : nothing
- Outputs: the score S
- Write the function in 3 steps: (1) simulate the rolling of dice n°1 and dice n°2, (2)
calculate the sum, (3) check if the two values are the same and, in that event, double
the sum to get the final score.

Hints :
- The command rand()*6 returns a random value between 0 and 6
- The function ceil(n) returns the nearest integer greater than or equal to n
- Combine them to get a random integer value between 1 and 6.
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Exercise 2
 The dice game with fair players

Use the template file simulation.m to build the simulator
- Initialization: set variables N=100 agents, T=50 time steps, and a vector called score
of length N, used to store the score of each player (initial values set to zero).
- In the update section, use the function fairRoll.m to update the score of player n
- Return the final vector score as an output.

Run the simulation. What is the mean score of all players at the end of the game? Use the
function max(score) to determine who is the winner.
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Exercise 3

The behaviour of a cheater:

Write a function called cheatRoll.m that return the score of a cheater:
-
Inputs : a variable called probaCheat representing the probability to have a
successful cheat.

Outputs: the final score S
Hints
Write your code in four steps :
1.
Determine the value of the first dice
2.
Pick a random number between 0 and 1, the cheat is successful if this number is
lower then probaCheat
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3.
Determine the value of the second dice according to step 2.
4.
Calculate and return the score S
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Exercise 4
 The dice game with one cheater:

Go back to your simulator. In the initialization section, add a new state called behaviour
with length(behaviour)=N , behaviour(i)=1 if player i is a cheater and behaviour(i)=0 if
i is a fair player. Set player n°1 as a cheater and all the others as fair players.

Modify the update section in order to call either fairRoll or cheatRoll, with respect to the
behaviour of the player n . Set the value of probaCheat to 0.6 (ideally, set it as a
parameter in the initialization section).

Run the simulation. Who is the winner? What is the score of the cheater and the average
score of the fair players?
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Exercise 5
 A framework for the simulator:

Create a new script file.

Use a for loop to repeat S times the simulation. At the end of each simulation, store the id
of the winner (the cheater has its id=1).

What is the winning rate of the cheater after S=100 games? Try to change the probability
of successful cheating (probaCheat) to reduce the winning rate to 75%.
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Exercise 6 (optional)
 Interactions and behavioural changes

In most of the case, the cheater does not cheat systematically, in order not to be too
suspicious.

Change the update section again, so that the cheater only use his special dice when
another player has a better score than him. Call the functions fairRoll or cheatRoll
according to the current score of the cheater. The behaviour vector should eventually be
updated as well, in case of a change of strategy.

2008-03-09
What is the cheater’s new winning rate ?
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