AGENT 2002

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AGENT 2002
Social Agents Ecology, Exchange Evolution

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The Interplay of Difference
Scott E Page De-Center for the Study of Com
plex Systems Center for Policy Studies - ISR Dep
artments of Political Science Economics
The University of Michigan-Ann Arbor
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This message is brought to you by
UM-Center for Research on Learning
and Teaching James S. McDonnell Foundation J
ames D. and Catherine T. MacArthur Foundation

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You Call That An Outline?

• What, how, when, and why I think

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You Call That An Outline?

• What, how, when, and why I think
• A new kind of Wolfram

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You Call That An Outline?

• What, how, when, and why I think
• A new kind of Wolfram
• The Classics

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You Call That An Outline?

• What, how, when, and why I think
• A new kind of Wolfram
• The Classics
• The Three Bears

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You Call That An Outline?

• What, how, when, and why I think
• A new kind of Wolfram
• The Classics
• The Three Bears
• Interplay

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You Call That An Outline?

• What, how, when, and why I think
• A new kind of Wolfram
• The Classics
• The Three Bears
• Interplay
• A Many Baby Bears Theory

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You Call That An Outline?

• What, how, when, and why I think
• A new kind of Wolfram
• The Classics
• The Three Bears
• Interplay
• A Many Baby Bears Theory
• Big Fun Ending

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What I Think?
The past couple of years I have been focusing
on the implications of diversity writ large.
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Diversity of Diversities

• wealth/energy
• ability
• information/sight
• preferences
• risk attitude
• type/species
• signal/tag

• representation of world
• tool kits
• charisma
• location
• gender
• culture
• identities (multiple)

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Games Theory Culture
Agents play multiple games simultaneously and
evolve strategies that share cognitive
subroutines. Consistent behavioral patterns evo
lve in communities of agents (culture emerges).
See Jenna Bednars web page.
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How I Think?
- agent based models - mathematical models -
bad metaphors
- facts
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When I Think?
(Tough last three weeks) - Orrie 30 months

- Cooper 12 months
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Why I Think (part 1)?
- War/Terrorism - Inequality - Crime - Drug
s - Sustainability - Growth - Culture - El
ectric Power
- Fun
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Why I Think (part 2)?
Dealing with the big stuff would seem to
demand understanding how the interactions
of diverse adaptive agents aggregate.

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S.O.S.O. Wolfram
30 Simple Rules Generate Randomness

110 Simple Rules Universally Compute
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A New Kind of Wolfram
He analyzes simple two type two neighbor models
on a one dimensional lattice. He creates amazing
pictures (not to mention really good randomness,
and if you spend a lifetime setting up the init
ial state a universal computer). And
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A New Kind of Wolfram
If he makes the models more complicated,
he doesnt find much interesting stuff.
Therefore, at its core the universe must be bot
h simple and complex.
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The Classics

• Our favorite agent based models of complex
  adaptive systems turn out to be (for lack of a
  better word)
  

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The Classics

• Our favorite agent based models of complex
  adaptive systems turn out to be (for lack of a
  better word)
  
• SIMPLE

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The Game of Life

• Behavior 1
• boredom/suffocate update rule
• States 2
• dead or alive
• Network
• fixed, torus with eight neighbors
• Dynamics
• synchronous updating

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BUT

• Flashers
• Gliders
• Glider Guns
• Figure 8
• Universal Computer

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Schellings Tipping Model

• Behavior 1.5
• move if unlike neighbors above a threshold
• States 3
• empty, type 1 or type 2 agent
• Network
• fixed, torus with eight neighbors
• Dynamics
• synchronous updating

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BUT
Jets
Jets
Sharks
Sharks
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The Bar Problem

• Behavior limited
• in workable models from small classes of rules
• Actions 2
• go or no
• Network
• none
• Dynamics
• synchronous updating

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BUT

• Ecology of Strategies
• Globally near efficient

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The Sand Pile

• Behavior 1
• topple if too high
• States 4
• but only need two
• Network
• fixed, torus with eight neighbors
• Dynamics
• synchronous updating

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BUT

• Self Organized Criticality
• Power Law
• Negatively Correlated Avalanche Sizes

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The Prisoners Dilemma

• Behavior limited diverse
• Miller two period memory automata
• States 4
• two by two game
• Network
• fixed torus
• Dynamics
• asynchronous updating

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BUT

• Evolution of cooperation
• Emergence of Tit for Tat
• Ecology of strategies All C and All D

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Diversity Model

• Behavior limited diverse
• basis in 2-dimensional space
• States NN
• each spot on lattice is a solution
• Network
• none
• Dynamics
• sequential updating

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BUT

• Marginal value of worker is arbitrary
• Any returns to scale possible
• Random group outperforms best group

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Sugarscape

• Behavior 1
• all agents follow simple random rule
• States infinite
• corresponding to sugar/spice level
• Network
• torus with rectangular grid
• Dynamics
• sequential updating

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BUT

• Nearly efficient exploitation
• Emergent prices
• Trade
• market makers

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The Three Bears
In case youve forgotten
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The Three Bears
Papa Bear too hot (hard..
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The Three Bears
Papa Bear too hot (hard.. Mama Bear too cold
(soft..

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The Three Bears
Papa Bear too hot (hard.. Mama Bear too cold
(soft..
Baby Bear JUST RIGHT!
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Exploration versus Exploitation
To search for solutions to difficult problems or
to evolve strategies in complex environments,
involves a tradeoff between explore and
exploit. Genetic Algorithm if the mutation rat
e and crossover probabilities are too high, no
structure gets exploited. Alternatively, if
the selection operator is too severe, the initi
al best is over exploited.
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Exploration versus Exploitation
value of solution
exploit
explore
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The Evolution of Evolvability
Bedau and Packard and others have shown that
you allow the mutation rate to evolve, then it
will settle into a region in which evolution can
be successful.
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The Evolution of Evolvability
value of solution
mutation rate
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The Edge of Chaos
There are three versions of the edge of chaos
1. Langtons lambda model 2. Kaufmans NK mod
el
3. The metaphor All have problems!!
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Langtons Lambda Model
In a Wolfram Style CA 000 0 idea count th
e of 1s 001 1 as it passes 3/8 you 010
0 start to see chaos 011 1 100 0 10
1 1 110 0 111 1
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Langtons Lambda Model
Problem (Crutchfield/Miller and Page)
Structured Rules 000 0 111 1 Unst
ructured Rules 000 1 111 0
CA rules in these two classes have the same lam
bda, all of the chaotic rules are unstructured.
Therefore, the dial metaphor is incorrect.
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Kaufmans NK Model
Binary Strings of length N. Contribution to
string value at bit depends upon bits at K other
sites. 010101000101 Bit 4 0101 .76321
As K increases, the best string value increases
up until K is large enough that the system
appears chaotic
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The Edge of Chaos
value of solution
K of interactions
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Kaufmans NK Model
The interactions are not evolved in the NK
model. When K is increased, the old interaction
s are thrown out and new random interactions are
created.
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Kaufmans NK Model
The interactions are not evolved in the NK
model. When K is increased, the old interaction
s are thrown out and new random interactions are
created. (When the radio goes in, the car goe
s out!)
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The Metaphor
The edge of chaos metaphor states that if
you have just the right amount of randomness
(or interaction) to support life and or
complexity than if you increase the randomness
(or interaction) you fall into chaos.
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The Edge of Chaos
value of solution
mutation rate/interactions
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The Long Mesa
value of solution
mutation rate/interactions
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The Edge of Boredom!!
value of solution
mutation rate/interactions
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The Number of Agent Types
In constructing agent based models, we often
find that as we increase the number of distinct
agent types, our models performance increases
and then decreases because the environment
gets too complex.
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Too many agents jumping on the bed
system performance
number of types of agents
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Topology and Space
Many agent models that use lattice structures
will not work if we place the agents in a soup
so that all of the agents interact with one an
other. Many become dull if we make the space l
arger so that not enough agents interact.
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Rock, Paper, Scissors
Rock All D Toxic E Coli Paper TFT Resistant
E Coli Scissors All C Sensitive E Coli We ge
t Stone Soup but a diverse lattice of
agents in models and in real world.
Kerr, Riley, Feldman, Bohannan (Nature 2002)
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Spacing Out Our Agents
complexity
alone lattice network soup

explore
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Spacing Out Our Agents
complexity
alone lattice network soup

explore
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Interplay A Synthesis

• Mutation Rate
• Langtons Lambda
• Interactions
• Number of Agent Types
• Spatial Arrangement

These together correspond to how many agents
you actually play
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Single Grazer Problem
Agent types choose subset of N fields to graze
Action 01001001110111 Payoff 0 if do not
graze 1 if sole grazer -big if more than
one grazer Artificial World each agent type h
as own GA
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Time to Efficiency
Periods 2 24 3 31 4
33 5 40 6 45 7 47 8
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9 56 10 63
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Meet The Flintstones Problem
Agent types choose subset of N fields to graze
Want to meet each agent C times
Action 01001001110111 Payoff -(M-C)2 for
each other type M inner product of actions
C constant Artificial World each agent typ
e has own GA
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Time to Efficiency
Periods 2 2 3 3 4
6 5 10 6 18 7 58 8
272
9 867 10 1650
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Why?
The single grazer problem satisfies the all
others as one property. The actions of all
of the other agents can be aggregated to look
like the action of a single agent
Agent 1 Action 00010010001 Agent 2 Action
10001100010 Agent 12 10011110011
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And so?
In the single grazer problem increasing the
number of agent types has almost no effect
other than through the mutation rate.
In the Meet the Flintstones problem no such agg
regation is possible. An agent needs to
know micro details of every agent action.
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Wait!
In the single grazer problem increasing the
number of agent types has almost no effect
other than through the mutation rate.
The implicit mutation rate increases linearly i
n the number of agent types Agents 12 N 0
1001110001101 Each bit mutates with probability
Nmutrate
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A Case Study Robustness
There are formal models that show a positive
relationship between diversity and robustness
There is also evidence that diverse ecosytems a
re the most robust as are diverse economies
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Diverse Robust?
There are formal models that show a positive
relationship between diversity and robustness
There is also evidence that diverse ecosytems a
re the most robust as are diverse economies
but.. diverse political systems often fall apart
.
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Wilma!! Stop this crazy thing!
Robustness Check Remove fields randomly
and see how long it takes the system to get back
to an efficient (or nearly efficient) stable
state. Answer it takes a while, especially as
the number of fields removed is increased.
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The Route Selection Model
Each agent type chooses a route to visit N sites
Action 8 4 7 2 5 1 9 3 0 6 Payoff minus the n
umber of agents you meet total
Artificial World each agent type has own GA
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The Route Selection Model
In Page (2001), I show that this model is
incredibly robust to the removal of sites. In
fact, if the routes that evolve consist of
multiple copies of the permutation group of
routes, then the system remains robust even after
removing sites
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Diversity Robustness
1234, 1243, 1324, 1342, 1432, 1423
2134, 2143, 2314, 2341, 2431, 2413
3124, 3142, 3214, 3241, 3412, 3421
4123, 4132, 4213, 4231, 4312, 4321
Get rid of 4 and you get four copies of
123, 132, 213, 231, 312, 321
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Aggregation Again!
In the route selection model, the other agents
can be collapsed into a super agent that has a
weight at each location. Once again, the micro
level actions of the other agents are not needed.
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A Many Baby Bears Theory
Claim In agent based models we want just the
right amount of interplay between our agents.

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A Many Baby Bears Theory
Claim In agent based models we want just the
right amount of interplay between our agents.

Too much interplay and we have a mess
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A Many Baby Bears Theory
Claim In agent based models we want just the
right amount of interplay between our agents.
Too much interplay and we have a mess Too lit
tle interplay and we have boredom
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A Many Baby Bears Theory
Claim In agent based models we want just the
right amount of interplay between our agents.
Too much interplay and we have a mess Too lit
tle interplay and we have boredom
Agent based models exist in the interesting
in between
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Adjusting Interplay

• Mutation Rate
• if other agents stay fixed it is as if an
  agent has no interplay with those agents

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Adjusting Interplay

• Selection Rate
• by reproducing own, create stability

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Adjusting Interplay

• Interactions
• more interactions means more potential interplay
  but the agents must change their actions and bump
  into one another

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Adjusting Interplay

• Agent types
• more agent types means more interplay if agents
  cannot be aggregated but can mean less interplay
  (by reducing the size of the integer problem) if
  others can be made into a super agent

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Adjusting Interplay

• Space
• more dimensions less interplay
• fewer connections less interplay
• soup lots of interplay

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Adjusting Interplay

• Timing
• synchronous increase interplay
• asynchronous reduce interplay (life killer)
• scale slow down you move too fast

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Adjusting Interplay

• Sophisticated Agents
• coordinate
• wait
• teach
• dimensional focus

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Adjusting Interplay

• Organizational Architecture
• one dimensional CA limits interplay
• hierarchy creates layered interplay and can have
  the same effect as changing time scales
  

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Adjusting Interplay

• Institutions
• multi-median voter versus elections
• Walrasian auctioneer versus spot markets
• local learning versus learning marginal agent
• reduce the action space

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Adjusting Interplay

• Emergence
• emergent structures can simplify
• emergence as all others as one

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The Big Question
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The Big Question
Evolution or Intelligent Design
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The Case for Intelligent Design
Were smart. Its not so easy to construct
a workable, interesting agent based model.

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The Case For Intelligent Design
Were smart. Its not so easy to construct
a workable, interesting agent based model

Did I mention that were really smart?
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The Case For Evolution
In many of our models, we implicitly allow
interplay to evolve through - selection on popu
lation levels - selection on type - tag evolut
ion - endogenous networks - fortuitous spaces
- endogenous interactions (strategies) -
evolving selection and mutation parameters
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The Difference of Interplay
Whether designed or evolved the amount of
diversity sustained in an agent based model
will be a function of spatial embedding,
interactions, mutation rate, and the ease of
aggregation.
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Pithy Famous Quote
Moderation is a fatal thing - Oscar Wilde
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Take Out Food
Complexity is a moderate thing
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Take Out Food
To be different is to be understood locally
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Take Out Food
When the many are one, the one can be many
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Final Poetic Thought
What are you going to do with your
one wild and beautiful life?
- m. owens