This document discusses various modeling frameworks for complex systems in the social sciences, including:
1. Game theoretic models which currently dominate but have limitations like multiple equilibria.
2. Agent-based and complexity models where agents follow simple rules and macro patterns emerge. Examples include flocking models.
3. Conceptual building blocks of models like search and exploration, emergence and self-organization, feedback loops, diffusion, networks, and dependency.
4. Specific diffusion models like SIR from epidemiology are discussed as ways to model the spread of ideas or behaviors.
The document emphasizes that combining different modeling frameworks in ensembles may be needed to capture real-world complexity.
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Complex Systems Models in the Social Sciences
1. Complex Systems Models
in the Social Sciences
(Lecture 8 + 9)
daniel martin katz
illinois institute of technology
chicago kent college of law
@computationaldanielmartinkatz.com computationallegalstudies.com
2. Part II of This Class
Starting on Monday,
Part II of this Course
Michael Bommarito Will Lead this Effort
In This Final Lecture Will:
Highlight the Various Forms of
Modeling Frameworks*
Try to Tie Together a Series of
Conceptual Building Blocks
*Drawn from Slides by Ken Kollman
4. What Are Models For?
“a precise and economical statement of a
set of relationships that are sufficient
to produce the phenomena in
question” (Schelling).
“Complicated enough to explain
something not so obvious or trivial, but
simple enough to be intuitive once it’s
explained” (Schelling)
Sometimes it is just Disciplined story-
telling - Sometime it can be more
5. What Are Models For?
Prediction
Conceptual clarity about assumptions
Insight about why we observe what we do
Evaluating Counterfactuals
10. Game Theory
Currently Dominant
Study of mathematical models of conflict and
cooperation among intelligent, rational
decision-makers (Myerson)
Rational---optimizing Bayesians
Intelligent--decision-makers know and
understand everything they do and we do
(NOT complete information)
11. The Primacy of
Nash Equilibrium
An “upper” solution concept, in
Myerson’s terms
If not Nash, then not
reasonable to predict
Problems:
Multiple equilibria
Importance of out-of-equilibrium beliefs
Actually doesn’t predict very well
15. Complexity Models
(1) Agents follow simple rules
(2) Emergence of macro patterns
Flocking Model is a Good Example
16. Justification for
Complexity Models
We can’t solve the models we want to
study given current analytical
techniques--computer is necessary
We believe we are studying agents who
adapt, or in some sense are boundedly
rational--computer is convenient but in
principle not necessary
Computational models are better at
modeling our contemporary world
17. Complexity Models
(3) Agents’ actions are interdependent
Can Be Modeled In Several Ways
Networks Are One Important way
18. Rule Encoding is Key
Agents Rules are Mixtures of
Global rules + Local rules
Simple Birth Rates is
Completely Global
Wolf-Sheep is a Mixture
Energy is indexed locally
But Each Agent is still
following same rules
32. Feedback = the return to
the input of a part of the
output (can be +, - or 0 )
33. negative feedback
negative feedback --> negative if the resulting
action opposes the condition that triggers it
This class of feedback is often described as
auto-regulating in so much as deviations from
the equilbriua are dragged back
34. Positive Feedback
positive --> if the resulting action builds upon
the condition that triggers it
These are the more interesting class of effects
Perturbations to the system can generate a
novel set of outcomes
35. A positive connection: !
!
For Full Example:
http://serc.carleton.edu/introgeo/models/
loops.html
!
The positive connection for a cooling
coffee cup implies that the hotter the
coffee is the faster it cools. The
variables Tc and Tr are coffee and room
temperature respectively.
36. a negative connection:!
!
the negative connection in the figure
below for a cooling coffee cup implies a
positive cooling rate makes the coffee
temperature drop. !
For Full Example:
http://serc.carleton.edu/introgeo/models/
loops.html
37. t h e t w o c o n n e c t i o n s
are combined yield a !
negative feedback loop !
!
coffee temperature approaches the stable
equilibrium of the room temperature.!
going around the loop the positive connection
times the negative connection gives a negative
loop feedback effect. !