Regional Modeling with GeoGraph Agents on Networks

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Regional Modeling with GeoGraph Agents on
Networks

• CIPEC
• Indiana University
• Thursday 17th January 2002
• Dr. Catherine Dibble
• Assistant Professor
• Department of Geography
• University of Maryland
• College Park, Maryland 20742
• cdibble_at_geog.umd.edu

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Background

• Currently Assistant Professor of Geography at the
  University of Maryland, College Park.
• Raised as a natural scientist, especially with
  respect to (wrt) biology, ecology, genetics,
  adaptive systems, and scientific rigor.
• Trained in formal economic theory at the U of
  Rochester in early eighties, especially wrt
  public finance, game theory, and trade.
• Twenty years of software design and development,
  eventually as a Director of Information Services
  (international patents).
• Santa Fe Institute Complex Systems Summer School.
• Geography ties it all together, via specialties
  in GeoComputation, spatial evolutionary modeling,
  and inventing and using agent-based computational
  laboratory tools for theorists.

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Agents

• Agent is a term used in Economic Theory and with
  Agent-Based Simulations
• An agent is any constituent entity whose behavior
  we wish to model, and its representation within
  the model.
• In particular, Agent is often used as a generic
  term to refer both to the real-world entity and
  to its representation within the model similar
  to object in GIS.
• For example, an agent may be, or may represent, a
  plant, an animal, or a person.
• Even a group such as a family, a country, or a
  corporation may be regarded as a behavioral agent
  for purposes of understanding a given system.
  Systems may be multi-level.

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Systems of Locally Interacting Agents
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Problem Domain

• General Problem Domain
• Modeling and understanding systems of mobile,
  heterogeneous socio-economic agents distributed
  on richly-structured geographic and/or
  organizational landscapes.
• Problem Domain Examples from Spatial Social
  Science
• Human-Environment Interactions, especially wrt
  local externalities and mechanisms for the
  sustainable use of common-pool resources.
• Evolution of Inequality (we can guarantee initial
  homogeneity)
• See DeCanio, Dibble, and Amir-Atefi, Management
  Science (2000)
• Regional Development co-evolution of settlements
  and networks
• Coordination Problems how agents coordinate (or
  not!) in space
• Dynamics of Complex Emergencies when/why/how
  things fall apart
• Spatially-Distributed Games and distributed Nash
  Equilibria
• Evolutionary Game Theory on richly structured
  landscapes

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Research Objective

• To design, develop, and begin using a
  general-purpose computational laboratory for
  conducting controlled experiments with models of
  mobile, heterogeneous, socio-economic agents on
  landscapes that are structured by one or more
  layers of spatial technology networks and/or
  organizational graphs.

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Outline

• Introduction, Problem Domain, and Objective
• The GeoGraph Computational Laboratory
• Spatial Small-world Synthetic Landscapes
• Globalization Processes on GeoGraphs
• Next Steps
• Computational Laboratory Practices

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GeoGraph Computational Laboratory

• GeoGraph software library extends
  the Swarm agent-based simulation system
  (www.swarm.org)
• GeoGraph Landscapes mathematical graphs
  (networks)
• synthetic BASE nodes and links (e.g. GRID,
  PEETers, RANDom, RING)
• spatial (with positive feedback, distance decay)
  small-worlds
  (extends Watts Strogatzs relational graphs,
  Nature 1998)
• GIS (networks, raster (already common with Swarm,
  cf Paul Box), o r both)
• GeoGraphically savvy Agents
• look around (global or local vision, may be
  restricted to network access)
• evaluate nodes according to desirability
  (optimize globally, satisfice, etc.)
• take action and/or move to a desirable node (or
  move randomly)
• may be homogeneous, multiple homogeneous classes,
  or heterogeneous within classes as well
• also may be adaptive and may have genes and/or
  memes
• may interact (e.g. trade, sneeze on one another,
  learn from one another)

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Grid GeoGraph(N49 T250)
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Radial Grid GeoGraph(N81 T60)
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Random GeoGraph(N25 K2 P0 T0)
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Ring GeoGraph (N25 P0.3 T100)
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Spatial Small-world Synthetic Landscapes

• Extension of Watts and Strogatz (1998) Nature
  paper on parameterized families of relational
  small-world graphs.
• Begin with a base configuration, such as a
  locally k-connected ring, randomly
  rewire each link with a very small probability p.
• Spatial small-worlds extend relational
  small-worlds by
• positive or negative weights with respect to
  distance
• positive or negative weights with respect to node
  degree
• a wild-card random weight tosoften the influence
  of the first two
• contraction factors to apply different costs or
  speeds to the various classes of small-world
  short-cuts (e.g. jet planes vs cars)

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Modeling Globalization on GeoGraphs

• Overall globalization refers to increased
  interactions at global scales. This can be
  separated into two components
• feasibility cheaper, faster spatial
  technologies
• response increased interaction at global scales
• GeoGraphs formalize feasibility via a contraction
  factor applied to the GeoGraph shortcuts, which
  reflects the technological advantage of
  short-cuts over base (e.g. RING) spatial
  technologies.
• Increased interaction is then implicit in the
  agents locational decisions with respect to
  access to one another.

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GeoGraph Globalization Landscapes

• Each RING edge is normalized to unit distance,
  wolog.
• Spatial small-world shortcuts have Euclidean
  distance.
• Shortcut distances are multiplied by a
  Contraction Factor
• 0 Star Trek Transporter (0 distance gt
  overlapping nodes)
• 1 Full Euclidean distance
• Log Range 0 0.02 0.04 0.06 0.08 0.1
  0.2 0.4 0.6 0.8 1.0
• 110 Controlled Families of Landscapes
• 10 Spatial Small-world RING landscapes (random
  number seeds)
• 11 Contraction Factors for each landscape

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Experimental Design

• 120 Agents play a 200-period locational game on
  60 Nodes
• Beginning with random configurations, agents
  optimize globally at each turn settle into a
  spatial Nash equilibrium.
• 10 Agent histories on each of the 110 landscapes
  (1,100 Obs)
• 30 agents in each sector, homogeneous within
  sector
• GROW, MAKE, SERV, INFO
• Identical populations of agents for all
  simulations.
• Collect local and global graph characteristics,
  agent populations, and agent objective scores
  (utility, happiness)

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Four Sectors in a Simple Locational Model

• GROW farmers / miners / loggers
  
• want to minimize local population density but to
  be near high-population market centers
• MAKE manufacturers / heavy industry
• want to maximize access to non-local MAKE and
  SERV
• SERV face-to-face direct service workers and
  retail shops
• want to maximize the local and nearby ratios of
  non-SERV customers to SERV agents
• INFO information and other footloose workers
• want to commute to MAKE agents for some work, but
  not to live too near their pollution (interesting
  tradeoff parameters!)
• want to be near SERV agents (e.g. Starbucks)
• may have preferences for optimal community size

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Sample Settlement Equilibria (T200)
No shortcuts Star Trek
Transporter Contraction 0.04
Shortcuts (c0)
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Hypotheses to Test

• First, as globalization progresses, do global
  graph characteristics explain more of the
  difference in equilibrium agent happiness in the
  landscape?
• AveHap a b1CPL b2Contraction
  b3Diameter e
•  
• Second, as globalization progresses, do local
  node graph characteristics explain more of the
  difference in agent population distributions
  (settlement patterns)?
• AgentPop a b1 RelNodeCPL b2
  Eccentricity b3 Degree
  e

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Geographic Structure Matters MORE as
Globalization Progresses
R-Squared
Spatial Technology Contraction Factor (increasing
Globalization)
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Geographic Structure Matters More than
Technological Improvements (e.g. Speed)

• AveHap a b1CPL b2Contraction
  b3Diameter e
• (1,100 Observations (global results from 1,100
  Simulations))
• Variable Parameter t Value Pr gt t
• Intercept 9.04 39.73 lt .0001
• Contraction - 1.27 - 4.01 lt .0001
• Diameter - 0.18 - 10.12 lt .0001
• Intercept 14.11 65.92 lt .0001
• CPL - 2.24 -34.81 lt .0001
• Contraction 10.75 26.32 lt .0001
• Diameter 0.39 19.24 lt .0001

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Next Steps

• Path-Dependence and the importance of prior
  structure
• Optimal configurations differ according to
  spatial technologies.
• To what extent do settlement systems evolve
  differently when you begin with modern spatial
  technologies (small contraction factors) from a
  random tabula rasa rather than from an historical
  equilbrium?
• Spatial Technologies and Economic Sectors
• Optimal configurations differ according to
  predominant economic sectors.
• To what extent do settlement patterns evolve
  differently when you begin with modern economic
  sectors (e.g. SERV, INFO) and modern spatial
  technologies rather than from an historical
  equilibrium evolved under GROW or MAKE regimes?

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Comp Lab Practices and Epistemology

• Within the domain of mobile agents on graphs,
  which problems are appropriate and which not?
• Dont try to do predictions. Dont use
  kitchen-sink models.
• Adaptive agents only if you are examining what
  they learn.
• Best Test effects of spatial processes on
  structure, structure on spatial processes, or
  (carefully) the co-evolution of each.
• Given a particular model, what are good
  laboratory practices for the experiments?
• Generate related families of controlled
  conditions.
• Use random numbers to run many iterations on
  related families of initial conditions that vary
  systematically.
• What can we know? Relationship of processes and
  structure.

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• Thank you!
• Questions?