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March 10 02006 Erb
Scott E PageUniversity of Michigan and Santa Fe InstituteComplex Systems, Political Science, Economics
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Agent Based Modeling
The Interest in Between
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Outline
What it is?
A ladder of models
A core question
The in between
Four uses
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What is it?
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The Spherical Cow
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A Whole Lotta Spherical Cows
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A New Kind of Science
Stephen Wolfram
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Wolfram’s 256 Automata
N X N X
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Rule 90
N X N X
2
8
16
64
Sum = 90
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Wolfram’s Findings
Simple rules can create
patterns like those in nature
randomness
computation
Summary: `it from bit’
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Conway’s Game of Life
X 5
76
41 2 3
8
Cell has eight neighbors
Cell can be alive
Cell can be dead
Dead cell with 3 neighbors comes to life
Live cell with 2,3 stays alive
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Examples
X
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A ladder of models
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Gell Mann’s Version
``Imagine how hard physics would be if electrons could think.”
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Model as Metaphor
Forest Fires & Bank Failures
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Forest Fire Model
At each site tree grows with prob p
Trees are good, lightening hits w/ prob q
Fires spread to neighboring trees
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Bank Failure Model
Make risky loans each period with prob p
Risky loans fail with prob q, but pay more
Failures spread to neighboring banks
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Example
Period 1: OOROOROOORRORPeriod 2: ROROOROORRRRR
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Example
Period 1: OOROOROOORRORPeriod 2: ROROOROORRRRR Period 3: ROROOROOFRRRRPeriod 4: ROROOROOFFFFFFPeriod 5: ROROOROOOOOOR
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The Bottom Rung:
Rule Aggregation
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A Phase Transition
rate of risky loans
yield
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The Second Rung:
Global Selection
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The ‘edge of chaos’
p*
yield
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The Third Rung:
Individual Adaptation
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What’s the matter here?
p*
yield
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Emergence of Firewalls
111O11O111O1111OO111
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The Top Rung:
Optimal behavior
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The Optimal Solution
1111011110111101111
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We follow routines
We select better rules
We respond and learn
We have it all figured out
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We follow routines: laundry
We select better rules: where we shop
We respond and learn: dating
We have it all figured out: tic tac toe
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A core question
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``What happens once we define the set of the possible and the rules of the game?’’
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Though policy analysis focuses on what happens if, we must also consider what happens if not.
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What goes up….
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Must come down.
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The Business EnvironmentIncentives: unfettered and induced
Regulations and restrictions
Technological change
Information
Global climate change
Demographic and preference change
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The in between
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How we answer the core question
Thick description (TD)
Simple models (SM)
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Agent based models enable us to explore the space in between the incredibly rich and complex real world and our stark models.
We can explore the attainability of outcomes, the robustness of functionalities, and the path dependence of systems.
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ABM can easily (and poorly) include
heterogeneity
networks and space
adaptation
feedbacks and lags
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Flexibility
Logical Consistency
TDABM
SM
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Four Uses
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ABM models complement SIR(S) models by including social networks, transportation systems, and agent level heterogeneity (genotypic and phenotypic) and adaptive responses
Math +
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ABM models allow us to test the implications of policies. Project SLUCE considered effects of sprawl policies on ecosystems at the exurban fringe.
The laboratory
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ABM models can be used as test beds for experiments with real people. Differences often minor -- TFT emerged in first experiments with both people and artificial agents.
The people alternative
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ABM models can be used to explore the implications of assumptions. From them we’ve learned how birds flock, how patterns form, and why some communicable diseases have waves.
The intuition builder
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Not if ABM, but how?
The economics of methodology
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This won’t happen by chance
