Complex Systems Models in the Social Sciences

(Lecture I)

Daniel Martin KatzMichigan State University

College of Law

Structure of this Course

Lecture - 9:00am - 10:00am

Lab - 5:00pm - 6:00pm

Structure of this Course

CC Little Michigan Lab@ Helen Newberry Hall

Theoretical Building Blocks

Empirical Investigations

Implementation

Applied Cases in Social, Political & Economic Systems

Lecture - 9:00am - 10:00am

Lab - 5:00pm - 6:00pm

Structure of this Course

Michigan Lab@ Helen Newberry Hall

CC Little

My Background

Assistant Professor of LawMichigan State University

Former NSF IGERT Fellow,University of Michigan

Center for the Study of Complex Systems(2009-2010)

PhDPolitical Science & Public Policy

University of Michigan(2011)

JDUniversity of Michigan

Law School(2005)

Blog Run with

Michael Bommarito II

JonZelner

Course slides will be

Posted Here!

Goals for the Class

Provide Introduction to Computational and Agent Based Approaches to Modeling

Provide a Solid Foundation in Implementation

Game Theoretic, Agent Based Models, Network Models, Ecological Models, etc.

Contrast Various Approaches Highlighting Benefits and Drawbacks

Be a Good Consumer of 3rd Party Implementation

Actually Implement Models Using Appropriate Software

Introduction to Complex Systems

Key Features of Complex Systems

Bottom up versus Top Down

Emphasizes dependancies between actors

Heterogeneous rather than Homogenous Agents

Complexity and CAS is not chaos theory

Emphasizes learning and adaptation by actors

Complex Systems Emphasizes

Simple behavioral rules generating complex and unforeseen outcomes

Self - organization / lack of top down control

Non-linearity, Emergence, Positive Feedback

Equilibrium and its Discontents?

Is an analytical solution up to the challenge?

What qualitative justification can be offeredfor assuming something is a fixed point attractor?

Is a representative agent model appropriate?

Does the solution concept scale to the scope of the problem?

CAS Focuses upon out of equilibrium solutions

Equilibrium and its Discontents?

When describing what would later be called the nash equlibrium to john von neumann in 1949, von Neumann famously dismissed it with the words,

“That’s trivial, you know. That’s just a fixed point theorem.”

“A Beautiful Mind” By Sylvia Nasar (1998)

clearly overstated but it is worth remembering that a fixed point based solution has limitations

Brief Introduction to Agent Based Modeling

Complex Systems and Agent Based Modeling

Agent Based Models are an Approach to Study Complex Adaptive Systems

However, the study of complex systems embraces a number of theoretical and empirical approaches

ABM’s are only one particular manner to execute the study of complex systems

Grand Father of Agent Based Modeling

Arguably the Most Important Mind of the 20th Century

Invented Game Theory

Helped Develop Atomic Bomb

Developed the Architecture of the Computer

2005 Nobel Prize Winner

Argues for Bottom Up Approach to Modeling In “Micromotives & Macrobehavior”

Outlines the Famous Schelling Segregation Model (aka the ‘Tipping’ Model)

Father of Agent Based Modeling

Other Important Contributors

John H. Conway

Developed the “game of life” a simple cellular automaton

Life is a universal cellular automaton capable of emulating any turing machine

Simple rules can generate Complex Environments

“Game of Life” offers lots of Important Complex Systems Principles

Other Important ContributorsRobert Axelrod

One of the top cited social scientists in world

Has made many contributions to the field of agent based modeling

http://www-personal.umich.edu/~axe/research_papers.html

Consult His Papers Page:

Axelrod & Tesfatsion Guide to Agent Based Models:http://econ2.econ.iastate.edu/tesfatsi/abmread.htm

Other Important Contributors

Joshua Epstein, Robert Axtell, John H. Holland

A Few Major Institutes & Centers

The Study ofComplex Systems

includes

Sociophysics

Natural Language Processing

Machine Learning

Network Science

Statistical Methods

Out of Equilibrium Models

Non Linearity

Scaling

Diffusion

Social Epidemiology

Information Theory

New Kind of Science

Computational Game Theory

Web Scrapping

Agent Based Models

Measuring Complexity

What is Complex Systems?

Complex Systems Offers

A Set of Tools

that allow us

to perhaps better understand

The Dynamics Underlyingthe Behavior of

Social, Political and Economics Systems

Taxonomy of Approaches

Data Analysis

FormalModels

Complex Adaptive Systems

Data Analysis

FormalModels

Complex Adaptive Systems

Data Analysis

This is the Era of “Big Data”

Decreasing Data Storage Costs

Increasing Computing Power

Fundamentally Altering the Scope of Scientific Inquiry

Highlighting the Data Deluge

2008 2009 2010

The Case for a Computational Approach

Complex Systems Output large amounts of Information

Need Methods that Scale to the Size and Scope of this Body of Information

Data Analysis

statisticalmodels

and methods

network analytic methods

text as

data

Measuring Complexity

Data Analysis

statisticalmodels

and methods

network analytic methods

text as

data

Measuring Complexity

More To Come On All of These Topics as the Course Continues

What is Complex Adaptive Systems?

Complex Adaptive Systems

Data Analysis

FormalModels

FormalModels

Formal Models

Othercomputational

Models

network models

AgentBased

Modeling

Why Generate Formal Models?

Formal Models v.

Data

The Evaluation of Counterfactuals

The Evaluation of Alternative

‘States of the world’

Cannot not be Exclusively Data Driven

A Few Examples ...

Theoretical Models and Computational Simulations

schelling’s segregation model

Axelrod’s Evolution of Cooperation model

We are interested in theData Generating Processes

For Example, Formal Network Models

Barabási-Albert Preferential Attachment

Othercomputational

Models

network models

AgentBased

Modeling

Complex Adaptive Systems

Data Analysis

FormalModels

statisticalmodels

and methods

network analyticmethods

text as

data

Measuring Complexity

More To Come Tomorrow!