Game Theory and ABM slides (PDF, 2.5 MB)

40 Pages·2016·2.46 MB·English

Modeling and Simulating Social Systems
with MATLAB
Lecture 5 – Game Theory / Agent-Based Modeling
Lloyd Sanders, Olivia Woolley, Dirk Helbing
Chair of Sociology, in particular of
Modeling and Simulation
ETH Zürich 31/10/16
Object-oriented Programming in MATLAB

MATLAB has support for object-oriented programming

However, we do not encourage to use this feature, as it
is not an efficient way of programming in MATLAB

Use of vectors and matrices instead of objects
 If you still want to have a look at how object-oriented programming works
in MATLAB:
http://www.mathworks.com/company/newsletters/articles/introduction-to-ob
ject-oriented-programming-in-matlab.html
Modeling and Simulating Social Systems with MATLAB 31/10/16
Schedule of the course
26.09
Introduction to
03.10
Modeling overview
MATLAB
10.10
17.10
Flash Talks
24.10
Introduction to social-
31.10
science modeling and
07.11
simulations
14.11
Working on projects
21.11
(seminar thesis)
28.11
05.12
Handing in seminar thesis
12.12
and giving a presentation
19.12
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Repetition: Cellular Automata

Cellular automata are abstract representations of
dynamics in discrete space and time

Reduction of complexity to simple microscopic
interaction rules based on neighborhoods

These simple properties are also the limitations: of cellular
automata: system dynamics cannot always be easily
reduced to microscopic interaction rules

Can be test beds for complex systems: for example
comparison of results of cellular automata and dynamical
systems
Modeling and Simulating Social Systems with MATLAB 31/10/146
Motivation for microscopic modeling

Some real world processes can be reduced to simple
local interaction rules (e.g. swarm Intelligence)

Microscopic modeling requires that dynamic components
of a system are ‘atomizable’ in the given context (e.g.
pedestrians behave like particles)

Represents a reductionist (or mechanistic) point of view in
contrast to a systemic (or holistic) approach

In line with methods that have fueled the success of
natural science research in the past 200 years

Game theory provides a powerful framework to formalize
and reduce complex (strategic) interactions
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Swarm Intelligence (1989)

Ant colonies, bird flocking, animal herding, bacterial
growth, fish schooling…
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Swarm Intelligence
Key Concepts:

decentralized control

interaction and learning

self-organization
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Boids (Reynolds, 1986)
 A boid is a simulated individual particle or object
moving about in a virtual space.
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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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Game Theory

Mathematical framework for strategic interactions of
individuals

Formalizes the notion of finding a ‘best strategy’ (Nash
equilibrium) when facing a well-defined decision situation

Definition and study of ‘games’

Underlying assumption is that individuals optimize their
‘payoffs’ (or more precisely: ‘utility’) when faced with
strategic decisions

Huge differences between game theoretic results for one-
shot games vs. repeated interactions
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