Complex Systems Models in the Social Sciences

(Lecture 9)

Daniel Martin KatzMichigan State University

College of Law

Part II of This ClassStarting on Monday,Part II of this Course will Focus on Applied Papers

Kyle Joyce from UC-Davis 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

Modeling Frameworks

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

What Are Models For?

Prediction

Conceptual clarity about assumptions

Insight about why we observe what we do

Evaluating Counterfactuals

Modeling Frameworks

General equilibrium

Differential equations

Decision theoretic

Game theoretic

Social choice

Graph Theoretic

Adaptive

Computational

Agent-based

Modeling Frameworks

General equilibrium

Differential equations

Decision theoretic

Game theoretic

Social choice

Graph Theoretic

Adaptive

Computational

Agent-based

SometimesYou Can

Build Ensembles

of theseFrameworks

Modeling Frameworks

General equilibrium

Differential equations

Decision theoretic

Game theoretic

Social choice

Graph Theoretic

Adaptive

Computational

Agent-based

We have Mostly

Focused on these ...

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)

The Primacy of Nash Equilibrium

An “upper” solution concept, in Myerson’s terms

If not Nash, then not reasonable to predict

Problems:Multiple equilibriaImportance of out-of-equilibrium beliefsActually doesn’t predict very well

http://www.youtube.com/watch?v=p3Uos2fzIJ0

Extensions

Axelrod’s computer tournaments!

Adaptive party modelsM. Laver (NYU Pol Sci) recent work

Formation of nation-states, empires

Social contagion (S.I.R. Models)

Complexity Models

(1) Agents follow simple rules

(2) Emergence of macro patterns

Flocking Model is a Good Example

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

Complexity Models

(3) Agents’ actions are interdependent

Can Be Modeled In Several Ways

Networks Are One Important way

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

Conceptual Building Blocks

Search / Exploration

Emergence + Self Organization

Path Dependence

Feedback

Conceptual Building Blocks

Diffusion

Dependence

How Do I Know That I Am On the Highest Peak?

Search / Exploration

Search / Exploration

Search / Exploration

Emergence + Self Organization

Path Dependence

Feedback

Conceptual Building Blocks

Diffusion

Dependence

phat-dependent

path-dependent

vs.

Search / Exploration

Emergence + Self Organization

Path Dependence

Feedback

Conceptual Building Blocks

Diffusion

Dependence

Simple Rules GeneratingComplexity

Absence of Top Down Control

Example:The Flocking Model

Search / Exploration

Emergence + Self Organization

Path Dependence

Feedback

Conceptual Building Blocks

Diffusion

Dependence

Feedback = the return to the input of a part of the output (can be +, - or 0 )

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

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

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.

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

the two connect i ons 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. !

Search / Exploration

Emergence + Self Organization

Path Dependence

Feedback

Conceptual Building Blocks

Diffusion

Dependence

Lots of Ways to Potentially

Model Diffusion

In General We are Interested in Dynamics

Yielding the Spreadof Some “Pathogen”

SIR Model is the Classic Compartmental model

from epidemiology

S (for susceptible)

I (for infectious)

R (for removed(i.e. immune or dead)

Lots of Other Variants

The SIS model

The SEIR model

Carrier state

http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology

The MSIR model

“Pathogen” could actually be a pathogen OR it could

be something else ...

Fads, Customs, Ideology,

etc.

Search / Exploration

Emergence + Self Organization

Path Dependence

Feedback

Conceptual Building Blocks

Diffusion

Dependence

We Covered this at great length ...

Networks are “dependency graphs”

Next Steps ...