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Claudio Cioffi-Revilla Center for Social Complexity George Mason University Fairfax, Virginia 22030 U.S.A. |
Nicholas M. Gotts Macaulay Institute Craigiebuckler, Aberdeen, Scotland AB15 8QH, U.K. |
November
7, 2002
Paper
prepared for the “Model-2-Model” Workshop on Comparing Multi-Agent Based Simulation
Models, Marseilles, France, March 31st-April 1st, 2003.
Copyright © 2002 Claudio Cioffi-Revilla and Macaulay Institute. All Rights
Reserved.
Abstract. In
this paper we compare models of two different kinds of processes in
multi-agent-based social simulations (MABSS): military conflict within a
states-system (GeoSim), and land use and ownership change (FEARLUS). This is a
kind of model-to-model comparison which is novel within MABSS research,
although well-known within mathematics, physics and biology: comparing objects
(in this case MABSS) drawn from distinct research domains, in order to draw out
their structural similarities and differences. This can facilitate research in
both domains, by allowing the use of findings from each to illuminate the other.
Based on the similarities between FEARLUS and GeoSim, we conclude by
identifying a new class of MABS (multi-agent-based simulation) models based on territorial resource allocation processes
occurring on a 2-dimensional space (which we define as the “TRAP2” class). The existence of
the cross-domain TRAP2 class of models in turn suggests that MABS
researchers should look for other members of the class, sharing some of the
properties or dynamics common to the GeoSim and FEARLUS models compared in this
study: a systematic comparison of a set of related models from a range of
apparently distinct domains should generate insights into both MABS modeling,
and the domains concerned.
This paper compares multi-agent-based social
simulations (MABSS) of two different kinds of processes. GeoSim (Cederman 2002;
Cederman, and Cioffi-Revilla 2002)
models military conflict within a states-system, while FEARLUS (Polhill, Gotts
and Law 2001) models land use and land ownership change. The paper arose from
the authors’ discovery that the two models, despite their apparently unrelated
subject matter, had a surprising number of similarities. The comparison of
entities or models drawn from distinct research domains, in order to draw out
their structural similarities and hence allow findings from each domain to
illuminate the other, is a standard research technique in mathematics and many
areas of natural and social science (Bak 1997, Davis and Hersh 1980, Ember and
Ember 2001; Landman 2000), but so far as we are aware, is novel within
Multi-Agent Based Simulation (MABS) research. The similarities (and
differences) between GeoSim and FEARLUS lead us to identify a new class of MABS
models based on territorial resource
allocation processes occurring on a 2-dimensional space (which we call
the “TRAP2” class), and to
seek further examples among existing models, and additional domains where the
model class might be useful.
Comparisons between MABS models can be made at three
main levels, which we will refer to as “structure”, “implementation”, and
“context”. Comparisons at the level of implementation
are the easiest to explain: they concern the computer software used in
performing simulations - primarily the
source code written by those presenting the model to the research community.
Comparisons at the level of structure
concern MABS models considered as abstract structures, defined verbally and/or
mathematically: two models implemented in different high-level languages, or
using different programming constructs in the same language, may embody the
same or similar abstract structure. Conversely, a given piece of software may
be conceptualized as the implementation of a range of different abstract
structures, as explained below. Comparisons at the level of context refer to the interpretations
given to the model’s abstract structure – the real-world entities and
relationships its elements are intended to represent – and the uses made of the
models in research, or in other types of application such as generating policy advice
(Bankes 2002) or facilitating participatory planning (Downing 2002). Our
concerns here are primarily in structural and contextual comparison, and within
the latter, in the interpretations given to models, and how they are used in
research.
There is no uniquely correct way to describe the
structure of a MABS model, but there are two related approaches which we find
particularly useful here. First, a MABS model (or any other kind of
discrete-event computational model) can be regarded as a homogeneous Markov chain (denoted simply as Markov chain hereafter) (Grimmett and Stirzaker1992, pp.194-5),
provided it has a countable number of distinct possible states, and fixed
(stationary) transition probabilities between pairs of states. A Markov chain
can be represented by a directed graph with labeled arcs, in which vertices of
the graph represent states of the model, arcs represent possible transitions
between states, and the arc-labels indicate the exact probability of each
possible transition. The state of a model at time t contains, by definition of a Markov chain, all the information
necessary to specify the probabilities of each possible state at time t+1[2].
Second, a MABS model may be thought of in terms of the types of objects (e.g.
agents, and parts of the environment) it consists of,
the numbers of each type, their properties and
relations, and a schedule of events which can change the inventory of objects,
and/or their properties and relations.
We can clarify both these approaches by describing
how they are related to each other. When a MABS model is described in the
literature, the description will generally mention a number of parameters,
different values of which produce variants of the model. For example, both
FEARLUS and GeoSim, along
with many other spatially explicit simulation models, have parameters
specifying how many “cells” (minimal spatial units) they contain, and which of
these share boundaries. Suppose all the parameters necessary to run such a
model are specified. The resulting fully
parameterized model will uniquely specify the probabilities of starting in
each possible initial state (the initial state is the state from which the run
starts), and the probabilities of all the possible transitions between states.
(If the initial state and transition probabilities have not been so specified,
then the supposed “fully parameterized model” cannot be described as a Markov
chain, and, as terminology is used here, it has not yet been fully
parameterized.) A MABS model as described in the literature can therefore be
identified with a (possibly infinite) set
of Markov chains, one for each permitted set of parameters.
One way to specify such a set is to describe the
permitted sets of states and transitions, in terms of the kind of object-level
description outlined above. A state of a fully parameterized model is then
analyzed into the set of model objects existing in that state, their current
properties, and their relations with each other. A transition between states is
defined in terms of the objects coming into existence and ceasing to exist, and
changes in the properties and relations of objects that survive the transition.
(It should be noted that two different object-level descriptions could turn out
to define isomorphic sets of Markov chains.)
In the next two sections, we describe FEARLUS and
GeoSim in object-level terms. These descriptions are intended to provide a
general understanding of the computational processes involved in each
simulation model, at a level sufficient to carrying out our comparative
analysis. More detailed descriptions, beyond the level of detail required here,
are published elsewhere (Cederman 2002; Polhill 2002[3]).
FEARLUS is a Swarm-based simulation (Swarm 2002). The
current version (FEARLUS-0.6.2) is an abstract model of land use and land
ownership. Land uses, biophysical properties of land parcels, and climatic and
economic conditions, are all represented as bitstrings, with simple matching
operations used to determine the economic return from a given land use at a
particular time and place. The main focus of research using FEARLUS so far has
been the relative success of different approaches by the model’s land managing
agents to land use selection (e.g. imitative versus non-imitative approaches)
in different kinds of environment (Polhill et al 2001, Gotts, Polhill and Law
2002). The conviction underlying this work is that land managers do not (and
indeed, cannot) act like the instrumentally rational agents of neoclassical
economics: they do not have the unlimited computational capacity this requires,
and their decisions are profoundly affected by social and cultural factors,
particularly their interactions with other land managers. A secondary research
theme has been the precautions necessary to avoid artifacts due to model
structure influencing outcomes in agent-based social simulation studies
(Polhill, Gotts and Law 2002a).
The objects in a
FEARLUS model at the start of a simulation run include:
·
A
Grid of Land Parcels[4].
·
The Grid may consist of Squares, equilateral Triangles, or equilateral Hexagons. Any Parcel edge is either
shared between exactly two Parcels, or (if the Parcel is at a free edge of the
Grid – see below) belongs to a single Parcel. The Grid is rectangular in shape,
consisting of xy Parcels (x and y integers). Each Parcel can be identified by its X and Y coordinates.
·
A Neighbor
Relation is defined on the Parcels. This specifies which pairs of Parcels
are considered Physical Neighbors. A
range of possible Neighbor Relations has been implemented, all but one of them
based on the X and Y coordinates. This can be described in
terms of three parameters:
· Topology. This may be Toroidal, Cylindrical, or Planar. In the Toroidal Topology, the “North” edge of the Grid is considered joined to the “South” edge, and the “East” edge to the “West”, so that all cells have isomorphic Neighborhoods. In the Cylindrical Topology just one pair of edges is joined, and in the Planar Topology, neither.
· Neighborhood Function. This specifies a Basic Neighborhood for each Parcel. For hexagonal or triangular Grids, this consists of those Parcels which share one of the given Parcel’s edges. For a Grid of Squares, the same may be true (von Neumann Neighborhood Function), or a Parcel’s Basic Neighborhood may be those sharing an edge or corner with it (Moore Neighborhood Function). For the Global Neighborhood Function, the Basic Neighborhood of each Parcel includes all others, making the Topology parameter irrelevant, and producing effectively non-spatial models.
·
Neighborhood
Radius. For
all Neighborhood Functions except the Global, the Neighbor Relation can also be
adjusted using the Neighborhood Radius, an integer, r. For the von
Neumann Neighborhood Function, the Physical Neighbors of a Parcel are those no
more than r squares directly to its
North, South, East or West (so the neighborhood forms an orthogonal cross). For
all other Neighborhood Functions, r specifies the maximum number of steps that can be taken from a
Parcel to one of its Basic Neighbors, without risk of leaving the Physical
Neighborhood of the starting point. So for a Moore Neighborhood Function and a
Neighborhood Radius of 3, for example, the Physical Neighborhood of a given
Parcel is a 7 by 7 square centered on that Parcel.
·
Each Land Parcel has a set of Biophysical Properties, encoded as a
bitstring and fixed for the duration of a simulation run; the length of these
bitstrings is a model parameter, the same for all Land Parcels. They are used
in investigating how the type and degree of the Environment’s spatial
heterogeneity affects the model’s dynamics.
·
The Global
Environment. This consists of the following:
·
The External
Conditions. Another bitstring (the length of which is again a model
parameter), representing a combination of climatic and economic conditions. The
External Conditions may change from one Year
to the next. Thus the Properties of Parcels vary across space but not time, the
External Conditions over time but not space.
·
Two numerical parameters which do not
vary over space or time: the Break Even Threshold (BET), which
specifies how much economic return or Yield
must be gained from a Land Parcel to break even, and the Land Parcel Price (LPP).
·
A set of Land Uses. Each Land Use is defined by a bitstring, the length of
which is the sum of the length of the Biophysical Properties and External
Conditions bitstrings.
·
A set of Land Managers (considered as representing households or firms, not
individuals). Each Land Manager has an Account,
initially having the value 0, and a Land
Use Selection Algorithm, described below. Each Land Manager is assigned an m by n
block of Land Parcels (m divides x, n
divides y). There are thus xy/mn Land Managers in the initial state
of the model.
·
One or more Subpopulations. A Subpopulation is a generator of Land Managers,
and is considered to represent a type
of Land Manager (for example, family farm households, or “agribusiness”
companies). When a Land Manager is created, it is assigned at random to a
Subpopulation, according to a probability distribution which is a model
parameter. Each Subpopulation in turn has an associated probability
distribution of Land Use Selection Algorithms, used to assign such an Algorithm
to a newly created Land Manager.
Considered at the implementation level, a
run of a fully parameterized FEARLUS model begins with a setup phase, Year Zero, in which Land Parcels are
assigned to Land Managers, and there is a random allocation of Land Uses to
Land Parcels. The Yield from a Land Parcel is calculated as described below,
but in Year Zero does not affect its Land Manager’s Account: it is used solely
as input to subsequent Land Manager decisions. At the level of abstract model
structure, Year Zero can be seen as implementing the stochastic selection of an
initial model state.
From this initial state, the run repeats
the following main loop, or Annual Cycle,
either a preset number of times, or until interrupted:
·
Agent
decision-making.
The Land Use for each Land Parcel is selected by its Land Manager,
using the latter's Land Use Selection Algorithm.
·
Calculation
of outcomes.
·
Calculation
of External Conditions. Bitstrings for any
number of Years may be stored in a file (to allow runs with identical External
Conditions to be compared), but otherwise the initial bitstring is determined randomly,
and each subsequent bitstring is produced from its predecessor by applying a
stochastic process to each bit independently. This process uses a parameter
called the Flip Probability, f. This specifies how likely each bit is to change. If f=0 the intial bitstring will be
retained throughout; if f=1/2, each
Year's bitstring is independent of its predecessors and the External conditions
are temporally uncorrelated. If 0
< f < 1/2, the External
Conditions change, but are temporally auto-correlated.
·
Calculation
of Yields. A Land Parcel’s Yield is determined by
comparing the concatenated bitstrings for the Parcel's Properties and the
current External Conditions, with the bitstring of the current Land Use, and
counting the matches
·
Harvest.
The Account of each Land Manager is adjusted. For each Land
Parcel owned, the Yield for that Parcel is added, and the BET subtracted.
·
Transfer
of territory from less to more successful agents.
·
Selection
of Land Parcels for sale. Each Land Manager
whose Account is in deficit puts up for sale (at the LPP) as many of their
worst-performing Land Parcels as necessary to clear the deficit, choosing at
random among Parcels performing equally badly.
·
Retirement
of insolvent Land Managers. A Land Manager
unable to clear their debt while retaining at least one Parcel, leaves the
simulation.
·
Sale
of Land Parcels. The selected Land Parcels are sold in
random order. One ticket in a lottery is issued for each Physical Neighbor of
the Parcel which belongs to a Land Manager with at least the LPP in their
Account (so Land Managers owning multiple Physical Neighbors get multiple
tickets), and one is left unassigned. A Land Manager must buy the Land Parcel (having the LPP deducted from their
Account) if selected. If the unassigned ticket wins the lottery, the Parcel is
given to a new Land Manager. This Land Manager starts with an Account of 0 after buying the Land Parcel.
When a Land Manager is created, either in
Year Zero or later, its Land Use Selection Algorithm is assigned. This is a
collection of three Strategies, along
with conditions for their use. The Contentment
Strategy is used when the Yield in the previous Year equaled or exceeded
the Land Manager’s Aspiration Threshold;
if this was not met, the Land Manager decides whether to use its Imitative Strategy or its non-Imitative Strategy according to its Imitation Probability.
The Contentment Strategy is to maintain
the same Land Use as before. The non-Imitative Strategy may rely on the Land
Parcel’s Biophysical Properties alone, or on some combination of these with the
External Conditions of recent Years. The Imitative Strategy makes use of
information about recent Land Uses and Yields from the Social Neighborhood: the Land Manager’s own Land Parcels, and those
belonging to Land Managers who own at least one Physical Neighbor of any of
these Parcels. Each Land Manager has a Memory
Length, specifying from how far back in time they can use information. See
Polhill (2002) for further details of the parameters that can be assigned to
Subpopulations to specify the probability distributions of Land Use Selection
Algorithms assigned to their members.
Most of the experiments undertaken with
FEARLUS so far have tested the relative success of different Land Use Selection
Algorithms in Environments differing in size, shape or Neighborhood Function
(Polhill et al 2002a), spatial and/or temporal heterogeneity (Polhill et al
2001, Gotts et al 2002), or Break Even Threshold (Gotts et al 2002). This has
been done by assigning Land Managers with equal probability to one of two
Subpopulations, with all members of each Subpopulation being given the same
Land Use Selection Algorithm.
GeoSim is a RePast-based simulation (RePast 2002),
following an earlier tradition of simulation models developed by political
scientists investigating international relations and world politics (Bremer
& Mihalka 1977; Cusack & Stoll 1990). The current version of GeoSim
(Cederman 2002) is a model of an inter-state or world system where sovereign
countries (nation-states) are composed of capitals and provinces and
interactions determine the rise and fall of territorial agents. Several
research questions have been investigated thus far using GeoSim, such as the
evolution of nationalism, the effects of technology, and the replication of
power laws of war (Cederman 2002; Cederman and Cioffi-Revilla 2002). The basic
computational framework of GeoSim is that countries have resources which they
then use for defensive and offensive purposes in a system of evolving sovereign
states. Over time, some states thrive and expand, while others collapse and
fragment or are conquered.
The objects in a GeoSim model at the start of a
simulation run include:
·
A Grid of
Territorial Actors
·
The Grid consists of a square array or lattice of
Squares or “primitive units”. These initial squares become the building blocks
of territorial states.
·
As the simulation evolves, each state (initially
consisting of a single square cell, similar to a city-state) forms as a set of
contiguous squares, or composite actor, one of which represents the capital of
the state and the others provinces (no longer a city-state, but a territorial
state). Initially there are many states with a single province (primitive
actors or city-states) and as the simulation evolves there are fewer states
with more provinces (composite actors).
·
Actors have three types of relations (graphs): local territorial relations (between von Neumann adjacent units), interstate
relations (between states), and hierarchical relations (between capital and
provinces). In principle, other relations can also be defined.
·
The Neighborhood Radius varies by type of relation.
For local territorial relations and for interstate relations the radius is one,
since only adjacent units (territorial) or adjacent states (interstate)
interact. The radius for hierarchical relations is given by the distance
between the capital and the farthest province (usually < 20).
·
At any given time each province-unit has an
associated amount of resources, and each composite actor (state) taxes each
province in relation to distance from the capital.
At the implementation level, the main simulation loop
consists of five stages:
·
Resource
updating
·
During the first stage the resource level of each
unit is updated by having the capital extract resources from however many
provinces it controls. Resources are extracted in logistically inverse
proportion to distance from the capital.
·
This computation also includes a technological
effect, which allows a capital to extract at a greater distance as the
simulation evolves, as well as gains or losses produced by the result of
frontier wars (see interaction stage below).
·
Resource
allocation
·
At the next stage each country (state) allocates
resources to each component province. The allocation is governed by two
mechanisms. First, there is an even share of resources distributed to
provinces. In addition, another share is allocated to provinces at war
(“fronts”), for both defensive and deterrent purposes. Cederman (2002) provides
examples of resource allocations.
·
Resource allocations are executed in parallel with
double-buffering and randomized order of execution.
·
Decision-making
·
Each state then decides what to do next, depending on
its state of alert and on the balance of power (resource ratios) at each front.
Unprovoked attacks occur only with a low probability (0.01) when the state of
alert is low for a given country
·
The probability of an agent province attacking a
target province belonging to an adversary country is a logistic function of the
ratio of resources between the neighboring provinces.
·
The decision-making stage is also executed in
parallel with double-buffering and randomized order of execution.
·
Interaction
·
Following the decision-making stage, the model then
executes all actions and computes the outcomes probabilistically, based on
resource ratios. For example, the probability of victory is computed as
logistically proportional to a favorable resource ratio, and approaches 1.0 as
the ratio approaches 3:1—a common rule of combat.
·
As a result, a country will have provinces with
battles either won, lost, or in stalemate (battles continue in the next round).
The first two outcomes set the stage for what happens next.
·
Structural
change
·
Finally, as a result of warfare, territorial changes
occur: each country may win or lose one or more provinces, or fighting may
continue in one or more provinces.
·
Note that, unlike earlier models (e.g., Cusack and
Stoll 1990), structural change in GeoSim affects only one primitive unit
(province) at a time.
After structural change has occurred a new
geopolitical landscape obtains and the process cycles back to the stage of
resource updating with new and old territories, as determined by the previous
cycle.
It should be emphasized that the three sets of
relations defined earlier (territorial or province-level, relational or
country-level, and hierarchical or intra-actor level) are key to understanding
the main simulation loop, the long-term dynamics, and how this system of
territorial agents evolves. In particular, decision-making is centralized at
the country level (relational interactions), as in the real world of interstate
relations, but battles are won or lost at specific unit sites or frontier
provinces (territorial relations). Thus, countries grow and decline in
non-trivial and complex ways that are entirely unpredictable when judging from
the simple computations that take place at each stage.
This section attempts to identify the most important similarities, and differences, between GeoSim and FEARLUS. The section begins at the “context” level: the interpretation given to the objects and events in the models, and the use made of them in research. Here, there are both important similarities, and major differences. When we turn to structural comparisons, we find far-reaching and, we believe, highly significant similarities in the overall structure of the two models. As we progress through more detailed aspects of model structure, we find more of a mixture of similarities and differences; at some points, we note topics for future investigation. The section concludes with a subsection on similarities and differences at the level of implementation.
Similar
worlds. Both models concern situations in which agents with
unlimited potential lifespan but liable to ‘die’ (be they households or firms
in control of farms or estates, or governing regimes in control of independent
polities), exercise exclusive control over parts of a two-dimensional space, make
decisions about the allocation of resources, and interact with their neighbors
in ways which include transfer of territorial control from the less successful
to the more successful agents. Such ‘worlds’ are also similarly ‘anarchic’, in
the sense that each consists of autonomous and autarkic agents that lack any
sort of supra-agent system of government (or ‘leviathan’ in a Hobbesian sense).
Of course, households or firms owning farms or estates are in general subject
to government authority, but in respect of the actions which are the subject of
FEARLUS, their choice of land use, they are in general free to make choices
independent of such authorities, and of their peers. Such an initial similarity
immediately raises issues regarding social dilemmas and conflict resolution
(Gotts, Polhill and Law, in press).
Spatial
and Organizational Scale. However, while both models deal
with the interaction between collective human agents controlling and using
parts of the Earth’s surface, the scale of the phenomena modelled is very
different. In FEARLUS, the agents are households or firms; in GeoSim, they are
states, or their governing elites. In
FEARLUS, the research intent is to gain a better understanding of land use
dynamics on a local or regional geographic scale, such as a county, province,
or perhaps a small to medium size country, given the total number of parcels;
in GeoSim the intent is to examine an entire ‘world system’, not necessarily a
particular region, since the number of cells is intentionally aimed to be
somewhere in the 100-300 range, similar to the total number of autonomous
polities (countries) in the modern international system.
Timescales.
FEARLUS has an explicitly calibrated timescale: each cycle of the simulation
represents a year; GeoSim is not explicit in this regard, although the
approximate range appears to be around 1-3 years, perhaps towards the lower end
(tax collection, military planning, seasonal battle factors, and so on).
However, further research is necessary in order to calibrate the GeoSim
timescale (Cioffi-Revilla 2002).
Military
versus Economic Competition. In the GeoSim domain of
interpretation, agents wrest territory from their neighbors by force; in the
FEARLUS domain, they merely acquire their neighbors’ territories following
economic failure. Of course, in the real world this distinction has cloudy
edges: a state may collapse due to economic failure, and then be divided among
its neighbors, while farmers may, in some times and places, force their
neighbors off their land by violence; but these aspects of the world are not
modelled in GeoSim and FEARLUS.
Research
intent. Research in GeoSim has concentrated on the overall
pattern of events occurring, and features of their statistical distributions
(e.g., the power laws that appear to govern the “size of wars”, Cederman 2002;
Cederman & Cioffi-Revilla 2002); research in FEARLUS, has focused instead
on the comparative success of different agent strategies under different sets
of parameters, and work on different ways of dividing up space and defining
neighborhood (Polhill, Gotts & Law 2001, 2002). As a consequence, FEARLUS
allows for heterogeneity of agent strategies, while GeoSim presently does not. Another consequence is the difference
in experimental methodology: simulation work in FEARLUS has concentrated on
finding statistically significant differences between the results of contests
between Subpopulations of agents in different environments; GeoSim has
concentrated on the emergent statistical features of distributions of events of
different sizes within simulations.
Validation.
At present, GeoSim has a closer relation to a coherent body of empirical
evidence (Cioffi-Revilla 1998, Cederman 2002; Cederman and Cioffi-Revilla 2002)
than FEARLUS. This is at least in part related to pre-existing differences in
the quality of data available: international politics and warfare are better
documented and studied than regional changes in land use and ownership: for
GeoSim, there was a coherent body of data about the size of wars requiring
explanation. All the same, numerous other aspects of GeoSim require further
validation (Cioffi-Revilla 2002: 1714-1716).
Agents and
Territory. In both FEARLUS and GeoSim, agents with unlimited potential lifespan compete for the control
of territory, which is divided into a regular grid of indivisible “cells”
(FEARLUS “Parcels”, GeoSim initial units or provinces). In both, all agents start off controlling
the same amount of territory (although this may be more than a single cell in
FEARLUS), and territorial expansion depends on being more successful in
decision-making than your neighbors. Again, neither model puts any limit on the
amount of territory one agent can acquire.
Main loops.
Both models have a “main loop” (see sections 2 and 3 above) that can be parsed
into three main computational phases:
(1) decision-making by the agents, (2) calculation of outcomes (calculation of
Yields in FEARLUS, interaction resulting in victories or defeats in GeoSim),
and (3) transfer of territory from the less to the more successful agents. The
GeoSim loop was described in five stages, but these can be parsed into three
for comparative purposes (the “Resource allocation” phase can be subsumed into
an expanded “Decision-making” phase, and the “Resource updating” phase
considered a piece of book-keeping after the “Interaction” and “Structural
Change” phases). The roughly parallel stages in the two loops are a key
element, along with other important grid and landscape features, in the class of
models that we discuss below.
Synchronous
actions by agents. In both models, all agents act
synchronously, in the sense that they all act without knowing the decisions of
their peers, although at some points in both models, the interacting effects of
different agents’ actions are dealt with by sequentializing those actions,
using a randomized order of execution.
Dual
neighborhoods. Both models also have a dual conception of
neighborhood: physical neighborhood
between cells, and social or political neighborhood between agents, derived from the physical
neighborhood relations of cells but distinct from it, (i.e., the relations
between farms in FEARLUS or polities in GeoSim). This means that both models
depart from the general cellular automaton rule of fixed neighborhood, so it is
not, even in principle, possible to translate them into standard cellular
automaton (CA) models (Gotts, Polhill and Law 2001). The CA-level processes
that arguably take place (between Parcels in FEARLUS and between provinces in GeoSim)
are completely dominated by the higher-order process between the main agents
where decision-making resides (farms and polities, respectively).
Spatio-temporal
hierarchies. The preceding feature—dual neighborhoods— produces a
three-level spatial hierarchy (parcels/provinces, farms/polities, world) as
another fundamental similarity. In turn, the existence of a spatial hierarchy
automatically raises questions such as (i) the distribution of cells across
farms/polities at any given time; (ii) the distribution of the frequency with
which different unit cells change “owners” over time, and (iii) similar
diachronic questions regarding the evolution of system composition and
distribution over time. There is also a parallel three-level temporal hierarchy: basic time-step,
agent lifespan, run-length (although in GeoSim the longest agent lifespan is
necessarily equal to the run-length). Both hierarchies provide fundamental
organization to the spatio-temporal structure of these models, and also suggest
numerous potentially insightful analyses that are yet to be undertaken (e.g.,
hazard rate models of intensity and duration variables; Cioffi-Revilla 1998).
Competition.
In GeoSim the competition between neighbors is direct, and essentially
zero-sum, given the territorial nature of competition; in FEARLUS, agents are
primarily ‘playing’ against external forces, and merely get the opportunity to
extend their territory when their neighbors fail. This micro-level difference
reflects the difference between the interpretations given to the models and
specifically, the different circumstances in which territories are transferred
between states and farms; it may or may not affect some macroscopic patterns,
such as power law distributions and other large-scale outcomes (see 4.7).
Regular
Two-Dimensional Grids. Both models are based on a
two-dimensional territorial space composed of a regular grid of identical
cells. GeoSim uses a grid of squares, with a toroidal topology and an initial
interaction network governed by a von Neumann neighborhood with radius 1. For
FEARLUS, this is one among a range of possibilities: most work has used a grid
of squares with a toroidal topology, but with an initial interaction network
governed by a Moore neighborhood with radius 1. Clearly, detailed outcome
comparisons between FEARLUS and GeoSim could be made using a GeoSim-type grid;
conversely, there is nothing to prevent GeoSim running with at least some of
the alternative types of grid FEARLUS uses. For example, hexagonal unit cells
are arguably more appropriate for representing political units, since the
average number of real world frontiers is closer to six than it is to four, and
military planners also use hexagonal grids (Cioffi-Revilla 2002: 1714-1716; Richardson
1961). Since so many MABSS use regular two-dimensional grids (often with
toroidal topology) we are inclined to omit this feature as uniquely distinctive
of the TRAP2 class as such, although it clearly remains a shared
feature of FEARLUS and GeoSim.
World
economies. In GeoSim, the total resources available for use in
acquiring new territory are fixed, and are transferred along with the
territory; in FEARLUS, resources are generated (or lost) in each cycle. This
difference implies that the “world economy” of the two models differs
substantially, since it is stationary in GeoSim (albeit not in distribution!)
but fluctuating in FEARLUS. Thus, FEARLUS seems rather more realistic in this
regard.
Physical
environments. In GeoSim, the physical environment external to the
agents is spatio-temporally homogeneous; in FEARLUS, it can (but need not) vary
over space and time. Again, clearly FEARLUS is (or can be) less stylized with
respect to physical environments, at least in the models that have been implemented
thus far. GeoSim and other Repast models may soon implement greater realism in
their physical environment (Padgett et al. 2002).
Unidirectional
causation. In both FEARLUS and GeoSim, the external
environment is immune to influence from the agents: they cannot change any of
its properties. In both models, the external environment can change over time,
but this change is exogenous: in FEARLUS, the External Conditions, representing
climatic and economic factors, can (and generally do) change, while in GeoSim,
there is the “technological effect” which allows extraction of revenues at
greater distances from the capital as time goes on.
Economic
starting point. In FEARLUS, all agents start out with equal wealth,
while a subset of GeoSim agents are given extra resources at the start of a
run. Conversely, however, the spatial heterogeneity of (most) FEARLUS models
means that some cells are more valuable than others, while all GeoSim cells
produce equal resources.
Decision-making
centrality. In GeoSim one cell of an agent’s
territory (set of cellular unit provinces) is where the ‘capital’ of the
country is located; FEARLUS has no equivalent. Thus, in political terms,
decision-making authority is explicitly centralized in GeoSim (as it occurs
with real countries in the international system). Political authority is not
decentralised in FEARLUS – the Land Manager makes decisions for all the Land
Parcels (cells) owned. However, the lack of a capital means that a farm could,
over the Years, wander freely around the map. Functionally, depending on the
parameters used, it is possible for there to be cells which an agent cannot
lose – but this is another significant difference between the two models.
Specifically, this can happen if the Land Manager’s algorithm guarantees a
positive net return (Yield minus Break-Even Threshold) on a particular Parcel,
and the Land Parcel Price is high enough to ensure that losses made elsewhere
can be made up by selling off lower-yielding Parcels, see Gotts et al (2001).
As computational objects, agents in both simulations
(be they Land Managers or regimes) posses a similar set of attributes and
methods (functionality), such as decision-making capacity, resource inventory,
territory, and agent territorial and relational connectivity.
Agent
Individuality. In any given fully parameterized model, however,
FEARLUS agents may (and generally do) have different decision-making
algorithms, while GeoSim agents all use the same algorithm.
Memory:
FEARLUS agents can in principle base their decisions on indefinitely distant
past events (although this capability has not been used in any published work),
while GeoSim agents consider only the present state of the world. For any given
FEARLUS agent and any fully parameterized FEARLUS model, however, there is a
limit on memory length.
Learning:
Neither FEARLUS nor GeoSim agents learn in the sense of changing their
decision-making strategies. (Strictly, there is provision for a very minor form
of strategy change in FEARLUS, but it is a legacy of earlier versions, never
used in published work.)
Imitation.
FEARLUS agents can imitate each other, while GeoSim agents do not do so.
Public
information about agents. Some of the information about
agents (notably, the territory they control and the allocation of resources
within that territory i.e. the distribution of forces among frontiers in
GeoSim, the Land Uses employed in FEARLUS), is public, that is, available to other agents. This has implications
for the implementation of the models in simulation tools such as Swarm and
Repast, which are based on the object-oriented programming paradigm. Polhill,
Gotts and Law (2002) suggest that this model feature may call for some
modification to that paradigm.
Information
environment. Both models are also similar in terms of their
heterogenous information environment. That is, agents in both models are
“surrounded” by information on other agents’ resources, location, costs, and
other data that is not homogenously distributed across the landscape. Again, further
implications of this similarity remain unexplored and therefore unknown at this
time.
Myopia.
Another similarity is that agents in both models are “myopic”, in the sense
that they worry only about the next move and are unaffected by any “shadow of the
future”. Myopic behavior is known to produce cumulative behavior and overall
results that can be fundamentally different from non-myopic, strategic behavior
guided by backward induction or other heuristic.
Choices
and Lotteries. Since each phase of the main loop is arguably an event, based on finite event analysis
(Cioffi-Revilla 1998: chs. 5–7), the loop can be modeled as a branching process, where nodes may be either choices (producing decisional
acts) or lotteries (producing states of Nature). Generally, therefore,
in our three-stage parsed process phase 1 is a choice (producing acts), while
phases 2 and 3 are lotteries (producing material results and territorial
transfers, respectively, as states of Nature). Clearly, the role of human agency
is therefore not uniformly distributed throughout the loop, but rather is
intermittent. Finite event analysis can uncover and highlight other features,
based on a more elementary decomposition of events (e.g., decision-making). The
formalization of the branching process implemented in each model makes it
possible to compare the two microscopic loop mechanisms in some detail, with
possible insights for understanding the emergent macroscopic dynamics.
(In)finiteness.
One considerable difference between the two models considered as Markov chains
or state-transition networks is that a fully parameterized FEARLUS model has
(in general) an infinite state-transition network, while all GeoSim models have
a finite one. This is a consequence of the fact that FEARLUS agents can
accumulate unlimited “wealth” in their Accounts, which have no parallel in
GeoSim. There are special cases of FEARLUS models with finite state-transition
networks: the simplest occurs when all Land Uses on all Land Parcels give a
Yield exactly equal to the Break-Even Threshold, so no Land Manager’s Account
ever contains a non-zero amount.
Sinks.
The GeoSim state-transition network has sinks: proper parts of the
state-transition network which can be entered from outside, but from which
there is no exit. Specifically, once a single agent has gained control of the
entire world, it will never lose it, and could only go through the motions of
collecting resources and allocating them to (non-existent) fronts. In general,
FEARLUS does not have sinks, although there are special cases in which they
exist. For example, if all Land Uses give Yields greater than the Break-Even
Threshold in all circumstances, all agents will get richer every Year, and
hence the model will enter a new sink, within the one it entered the previous
Year. Even if this is not the case, particular Managers can gain permanent
control of particular Parcels, as already noted.
Further
network properties. We can consider further properties
of the state-transition network such as connectedness, centralization,
diameter, fractal dimension, entropy, and network uncertainty, It should be
noted that, although these are attributes in a computational object sense, they
may not all be implemented as such. Nonetheless, these attributes should be
investigated further.
Territorial
configurations and changes. At a higher structural level, we
can characterise the state of a fully parameterized model at the end of each
cycle simply in terms of the division of the grid into territories, and (in the
case of GeoSim) of the capitals. Considered at this level, both GeoSim and
FEARLUS have a finite set of possible territorial configurations, and for grids
of the same size, GeoSim’s set may be larger, since for a given division into
territories, there are generally multiple distributions of capitals in GeoSim.
Offsetting this, however, is the fact that a FEARLUS territory need not be a
single connected piece, while a GeoSim territory must be (indeed, it must be
“line connected” in the sense of Gotts (2000), that is, not divisible into two
parts sharing only isolated boundary points).
A cell newly added to a FEARLUS territory will always be a physical
neighbor of a cell that is already a member, however.
Another difference at this level is that GeoSim
agents can both gain and lose cells in the same cycle, while FEARLUS agents
cannot.
Demographics.
As a corollary of these life-and-death dynamics over ‘time’ (cycles), both
models are capable of generating ‘life tables’ or ‘survival’ data pertaining to
the evolution (births and deaths) of agents, be they land managers or regimes.
From such raw data it is possible to calculate a set of statistics (e.g.,
moments) and probability functions (e.g. survival functions, hazard rate
functions, and other functions based on classical cumulative density functions
and probability density functions) for agent populations. Very little of this
work has actually been done, although the methodology is well-known and can be
readily applied (Cioffi-Revilla 1998).
Power
laws? Power law analysis offers an important and so far
underutilized means for assessing issues of validity, universality and
calibration in MABSS (Cioffi-Revilla 2002). Visual inspection of both models
suggests that perhaps some variables (e.g., size of territorial units; size of
changes, etc.) may obey power laws of the form ƒ(x) ~ x–f,
where x is the size variable and f
is the fractal exponent or dimension. Cederman (2002) and Cederman and
Cioffi-Revilla (2002) report some preliminary power law results for the
occurrence of warfare in GeoSim. It is reasonable to conjecture that, given the
other similarities, FEARLUS may also yield power laws.
Simulation
software. FEARLUS and GeoSim are based on similar simulation
tools—Swarm and RePast, respectively. RePast was developed as an improvement on
Swarm. Indeed, RePast borrows much from the Swarm simulation toolkit and can
properly be termed “Swarm-like.” In addition, RePast includes such features as run-time
model manipulation via GUI widgets first found in the Ascape simulation
toolkit’ (RePast 2002).
Formal social science models can be classified in
innumerable ways: the common ground between GeoSim and FEARLUS is sufficient to
make it useful to define a class to which they both belong, for which it may be
possible to arrive at useful analytical results (say, in terms of a structured
set of possible regimes of behaviour the models could show), and define common
approaches to areas such as sensitivity analysis, study of simplified cases
(such as what happens if transfers of territory are made using simple lotteries
instead of strategic interactions), avoidance of artifacts, and searches for
parameter settings which give particular outcomes.
We define TRAP2 models as having the
following minimal characteristics:
1. An
exclusive relationship linking each agent to the territory it controls at any
one time (i.e., any piece of territory has just one owner at a time).
2. No
agent movement or location within the territory held.
3. A
mechanism for the transfer of territory between agents – specifically, from
less successful to more successful agents. (Agents may or may not be assigned a
core territory with which they have an indissoluble connection: GeoSim
distinguishes one cell as the agent’s ‘capital’, while FEARLUS makes no such
provision.)
4. A
decision-making process in which each agent determines how the
territorially-linked resources it currently controls are to be used to advance
the agent’s interests.
5. Agents
with unlimited potential lifespan but the possibility of ‘death’.
6. Synchronous
action by the agents.
7. A
fixed configuration of ‘atomic’ two-dimensional regions (cells), the minimal
bits of territory transferred between agents. (Of course, the real world
doesn’t have such a structure, so this is a significant idealisation.) The
cells may, but need not, form a regular lattice. Each cell has a set of
boundary edges, ending in vertices: each edge either belongs to a single cell,
or is shared between exactly two cells.
8. A
symmetric physical neighborhood relation defined on the cells. The cell
configuration is connected in terms of this neighborhood: that is, there is a
path from any cell to any other, in which each adjacent pair of cells are
physical neighbors according to the definition of the physical neighborhood
relation.
9. A
many-to-one relation linking cells and agents, arising necessarily from points
1, 3, 7 and 8.
10. Arising
from this many-to-one relation between cells and agents, two distinct but
related levels of neighborhood: between cells (fixed throughout a model run),
and between the territories owned or controlled by agents (varying over
simulated time).
11. An
indefinitely repeated cycle of events, subdivided into a specified sequence of
phases which includes phases of strategy choice, calculation of outcomes, and
transfer of territory.
12. A
fixed set of possible decision-making algorithms for agents, in two senses:
individual agents do not alter their decision-making algorithms, and all agents
in a given fully parameterized models will draw their strategies from a limited
set: there is no mechanism for generating novel strategies in either model.
Within these characteristics, we can attempt to
distinguish those which appear to derive from fundamental features of the
real-world domains which the two models are intended to represent (1-6 above),
and those which are convenient simplifications (adopted in order to make the
models simpler to design and understand), or
which arise from such simplifications in combination with the
fundamental features (7-12 above). It will be seen that several among the
second group of common features arise in one way or another from treating the
world as discrete in space and time, rather than as continuous. It should be
noted that this is not the case for
point 6, synchronous action by the agents: in the real world as in these
models, agents interacting with each other must frequently act in ignorance of
the decisions and current actions of their peers. It is also worth noticing
that points 8 through 10 would have close counterparts in continuous models of
the same domains: if place A is near place B, then B is near A, whether A and B
are discrete, well-defined cells or not, and in the real world, there are
neighborhood relationships both between polities or farms, and between
locations within these discrete, anthropogenic divisions of the Earth’s surface.
Finally it can be argued that indefinitely repeated
cycles of action, interaction and territorial transfer (point 11), and the use
of limited and stereotyped sets of alternative actions (point 12), are
reasonable first approximations to the way in which human and animal
collectives interact with each other.
Thus most of the main similarities between FEARLUS
and GeoSim can be traced, at least in part, to the common features of the
domains they are intended to illuminate. These features may seem obvious in retrospect,
but we are not aware of any previous exploration of parallels between the
domains of international power politics and rural land management. This prompts
us to ask what other domains have, or could have, models falling within the
TRAP2 class. Since the most important common features of the domains
are competition for resource-providing territory between agents with unlimited
potential lifespan, we suggest the following domains as among the most
promising:
·
Competition between non-state human social groups
which occupy and exploit territory (hunter-gatherers, non-state
agriculturalists, criminal gangs in cities).
·
Competition between political parties in
constituency-based elections.
·
Competition between non-human social groups (wolf
packs, baboon troops, ant colonies). In most of these cases, however, there is
an effective limit to the size of social group that can remain coherent, and
thus on the territory that can be controlled.
·
Models of ecological competition between clones (i.e.
genetically-defined plant, fungal or bacterial individuals which can grow
indefinitely, or at least for very long periods, without giving rise to new,
genetically distinct individuals by sexual reproduction).
·
Competition over evolutionary time between species
with ecological requirements that are sufficiently similar to prevent their
co-occurrence in a single area.
Many domains in which MABS models are or might be
used would not be suitable for TRAP2 models. Clearly this is so if
the spatial relationships between the agents are not important. However, it may
be most useful to consider a few “near miss” domains, which share some features
with those suitable to TRAP2 modelling,
but lack at least one key characteristic, for example:
·
Domains where the agents concerned have a potential
lifespan shorter than the time over which events are to be modelled – for
example, competition between members of solitary, territorial species.
·
Domains where indefinitely long-lived agents compete,
and are located in space, but do not control exclusive territories: for
example, firms competing for market share, or species which compete for some
type of resources, but have sufficiently different ecological roles to coexist
spatially.
·
Domains where there is competition, territorial
control and neighborhood, but territorial expansion is absent or unimportant.
In fact, many abstract MABSS of
interaction and competition, such as Kirchkamp (2000), fall into this
category, but it is less easy to think of real-life cases.
·
Competition between languages, religions, or other
cultural forms: potentially immortal
entities which do have a degree of location in space but do not, in the general
case, entirely exclude each other. However, in special cases – of effectively
enforced intolerance – this domain might be suitable for TRAP2 models.
·
“Competition” between land uses for limited space, as
modelled within the CLUE framework, for example (Verburg, de Koning, Kok,
Veldkamp and Priess 2001). In this case, the “competitors”, which might be
identified as agents (CLUE does not do so), are in fact choices open to the
“real”agents, the land managers.
Our next steps in this research are:
(1) Continued
work on the similarities and differences between FEARLUS and GeoSim. Since both
models are regarded as work in progress, it may well be possible to design
future versions so that FEARLUS scenarios can be run within GeoSim, and vice
versa. We will also work on the transfer of ideas and techniques in both
directions: some of the possibilities have already been mentioned.
(2) A
survey of existing MABSS within our “home domains”of land use and international
politics, to identify those which fall within or on the border of the TRAP2
class, and to determine whether those within the class do in fact appear
to form a sizeable and coherent group.
(3) A
survey, more detailed than the brief outline given here, of other possible TRAP2
domains.
(4) Further
consideration of “near miss”domains such as those listed above.
(5) Steps
1-4 will enable us to refine our description of the TRAP2 class of
models. At some point in this process, it will be useful to move from the kind
of natural language definition given above, to description in some suitable formal language, perhaps
similar to PMML, which is being developed to describe statistical and data
mining models (Data Mining Group 2002). Development and use of suitable
formalisms should assist in the cooperative development of generally useful
descriptions and classifications of MABS models; however, if the move from
natural to formal language is made too early in refining a modeling concept,
the chosen formalism may play too large a role in shaping the outcome.
(6) A
search for theoretical insights and modelling techniques which can be
transfered between TRAP2 domains.
By using GeoSim and Fearlus to identify and describe
this broader class of TRAP2 models, we believe we have advanced our
understanding of both model domains, of the model class itself and of MABS
models in general; and gained insights on a variety of aspects of modelling
generally not considered through single-model analysis. We believe this paper
illustrates one way in which MABS models can facilitate interdisciplinary
collaboration and exchange of insights – in this case, between the domains of
international politics and rural land management. The opportunity to undertake
this study for the M2M Workshop has certainly been scientifically rewarding and
worth extending.
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[1] Authors are listed alphabetically. The present work was completed with partial support from
the Complex Systems Network of Excellence (Exystence), FET-IST European
Communities grant IST-2001-32802. Cioffi was
supported by the Center for Social Complexity at George Mason University. Gotts
was supported by the Scottish Executive Environment and Rural Affairs
Department. The authors are grateful to the authors of the simulation models
compared in this study, but they are solely responsible for any errors of
interpretation.
[2] Note that this does not prevent, for example,
agents in a MABS model using stored information about earlier times: the
contents of the agents’ memories of times t-1,
t-2… themselves form part of the
model’s state at time t.
[3] The description of FEARLUS differs in some
respects from that given in Polhill et al (2001); this reflects changes to the
model made since that paper was written. Polhill (2002), being a user guide,
describes the model at the implementation level. Some features of the
implementation that have never been used in experiments, and some which are not
regarded as part of the structure of the model for the purposes of this paper,
are ignored or described only in outline here.
[4]A number of terms
will be used to refer to elements and aspects of FEARLUS models, some of which
could also refer to real-world entities. In FEARLUS model terms, each word
begins with an upper-case letter (e.g, “Land Manager”). Each such term is
italicised when first used.