Diversity: Optimality and Equilibria

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Scott E Page University of Michigan and Santa Fe
Institute Complex 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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Wolframs 256 Automata

N X N X
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Rule 90

N X N X
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8
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Sum 90
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Wolframs Findings Simple rules can
create patterns like those in
nature randomness computation Summary
it from bit

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Conways Game of Life

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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2
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X
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Examples

X
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A ladder of models

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Gell Manns 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 OOROOROOORROR Period 2 ROROOROORRRRR
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Example
Period 1 OOROOROOORROR Period 2 ROROOROORRRRR
Period 3 ROROOROOFRRRR Period 4
ROROOROOFFFFFF Period 5 ROROOROOOOOOR
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The Bottom Rung Rule Aggregation

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A Phase Transition
yield
rate of risky loans
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The Second Rung Global Selection

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The edge of chaos
yield
p
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The Third Rung Individual Adaptation

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Whats the matter here?
yield
p
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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 Environment Incentives unfettered
and induced Regulations and restrictions Technol
ogical 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 heterogeneit
y networks and space adaptation feedbacks and
lags

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TD
Flexibility
Logical Consistency
ABM

SM
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Four Uses

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Math

ABM models complement SIR(S) models by
including social networks, transportation
systems, and agent level heterogeneity (genotypic
and phenotypic) and adaptive responses
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The laboratory

ABM models allow us to test the implications of
policies. Project SLUCE considered effects of
sprawl policies on ecosystems at the exurban
fringe.
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The people alternative

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.
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The intuition builder

ABM models can be used to explore the
implications of assumptions. From them weve
learned how birds flock, how patterns form, and
why some communicable diseases have waves.
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The economics of methodology

Not if ABM, but how?
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This wont happen by chance