2010-03-22 851-0585-04L – Modelling and Simulating Social Systems with MATLAB Lesson 5 –...

2010-03-22

851-0585-04L – Modelling and Simulating Social Systems with MATLAB

Lesson 5 – Introduction to agent-based simulations

A. Johansson & W. Yu

© ETH Zürich |

2010-03-22 A. Johansson & W. Yu / [email protected] [email protected]

Send us an abstract of your project.

Don't re-invent the wheel but try to build upon

existing models.

Start simple and extend functionality.

Look at project reports from previous semesters.

Projects

2

2010-03-22 A. Johansson & W. Yu / [email protected] [email protected] 3

Lesson 5 - Contents

Swarm intelligence

Human cooperation and coordination

How to develop a multi-agent simulator


Swarm Intelligence

4

Decentralized control

Interaction and learning

Self-organization


Boids (Reynolds,1986)

5


More information: http://www.red3d.com/cwr/boids/

6

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


Human Cooperation

Prisoner’s dilemma

7

15,15 20,0

0,20 19,19


The Evolution of Cooperation (Axelrod,1984)

Tit for tat

Shadow of the future

8


Coordination

1,1 0,0

0,0 1,1

9


Learning

Imitation

Reinforcement

Best reply

10


From Factors to Actors (Macy,2002)

Agents are autonomous

Agents are interdependent

Agents follow simple rules

Agents are adaptive and backward-looking

11


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…


Programming a simulator

Agent based simulations

Time line

Characterized by a state (or states)

(location, dead/alive, color, level of excitation)

Time t Time t + dt

State update

According to set of behavioral rules

New state

T1 T2dt



Agent based simulations

Characterized by a state

(location, dead/alive, level of excitation)

Time t Time t + dt

State update

According to set of behavioral rules,

including neighborhood

New state

Time line T1 T2


Programming a simulator Programming an agent based simulator often goes in five steps

Initialization- Initial state; parameters; environment

Time loop- Processing each time steps

Agents loop- Processing each agents

Update- Updating agent i at time t

Save data- For further analysis

Initialization

Time loop

end

Save data

Agents loop

end

Update state



Step 1: Defining the initial state & parameters

% Initial state

t0=0; %begining of the time linedt=1 ; %time stepT=100; %number of time steps

%Initial state of the agentsState1 = [0 0 0 0];State2 = [1 1 1 1];etc…



Step 1: Defining the initial state & parameters

% Initial state

t0=0; %begining of the time linedt=1 ; %time stepT=100; %number of time steps

%Initial state of the agentsState1 = zeros(1,50);State2 = rand(1,50);



Step 2: Covering each time step

% time loop

For t=t0:dt:T

What happen at each time step?- Update environment- Update agents

end



Step 3: Covering each agent

% agent loop

For i=1:length(States)

What happen for each agent?

end



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;

elseState(i)=0;

end

Use sub-functions for better organization!!




% update% Each agent has ‘proba’ chance to switch to state 1

randomValue=rand();

if (randomValue<proba)State(i)=1;

elseState(i)=0;

end

Define parameters in the first part!!




% Initial state

t0=0; %begining of the time linedt=1 ; %time stepT=100; %number of time stepsproba=0.6; %probability to switch state

Define parameters in the first part!!



Step 5: Final processing

% Outputs and final processing

propAlive = sum(states)/length(states);And return propAlive as the output of the simulation.


>> p=simulation()

p =

0.54

>> p=simulation()

p =

0.72


Running simulation



Alternatively : a framework for the simulator

% Running N simulations

N=1000 %number of simulation

for n=1:Np(n)=simulation();

end

Use a framework to run N successive simulation and store the result each time.



Alternatively : a framework for the simulator

>> hist(p)

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