Anthropological Mapping in Socio-Natural Systems: META Game Theory
Dallas F. Bell, Jr.
Abstract: The praxis of mapping individual, nation-state, and
global decision-making behavior can be demonstrated nonlinearly in
the field of ecology. This method incorporates the tools of latent
semantic and fuzzy analysis to apply specific geo-spatial data
toward the elements, factors, and variables found in systematic
political science. Game theory techniques are used to unify the
anthropocentric disciplines of theology, epistemology, psychology,
sociology, and eschatology—META games. Therein lies the essence of
socio-natural systems to which (co-)evolutionary processes are studied.
Given the heuristic understanding that to evolve infers movement to a
state of higher order, mankind's increased knowledge and subsequent
technological advancements are the examples of evolving presented. Those
dynamic changes occur in societies from natural law in varying degrees.
Therefore, the method of determining why this differentiation between
individuals and groups eventuates is important. This interdisciplinary
paper analyzes macro and micro human motivations and potential roles
in sustainable development. The respective behavioral arcs combine to
form waves, which create the area of the function. That area provides
historical evidence for stochastically predicting future potential.
Using this method should enhance the ability of policy makers to apply
resources and energy due to greater forecasting accuracy.
Keywords: Ecology, Anthropology, Mapping, Systematic Political Science,
If one has been given the task of allocating resources, how would
he or she prioritize the distribution of those limited assets?
One would hope that they be used in the most efficient manner
possible. Ecologists know that different organisms do not act and
react to their surroundings monolithically. Anthropologists are also
aware of diverse human actions and reactions in socio-natural systems.
For example, the American botanist George Washington Carver found
hundreds of human uses for the peanut. He didn't bother to patent those
discoveries, stating that his ideas came from God to help others increase
in knowledge and well-being. Recent events have brought the concept of
terrorism to the forefront of global consciousness. Unlike Carver, those
people who are involved in terrorist activities do not invent but claim
to have divine inspiration to use benevolent tools (e.g., cell phones,
automobiles, and aircraft) to harm even small school children.
Why and how these opposing individual behaviors occur regarding the (co-)
evolutionary processes of knowledge and technology will be examined
herein. Additionally, focus will be given to those behaviors'
creations of respective egalitarian First World and oppressive Third
World socio-natural systems.
Understanding this focus requires familiarity with the concepts and
symbols of systematic political science. Man cannot do things contrary to
natural laws, such as dematerialize, so game theory is used to indicate
the relationship of individual and societal decision-making behavior
to realistic possibilities. Systematic political science can easily
be explained using the acronym TRICE: the Theology of each individual
produces the authority/standard to process information, which becomes
their Rational epistemology. That rationality is applied to meeting
the hierarchical common Individual needs--survival, economic security,
love and affection, status and self-esteem, and self-actualization.
Those individuals join others with the same rationality and needs to
create Collective behavior that supports a correlating societal level
in a political system. These First, Second, or Third World systems are
based on the Eschatological faith of the future asymmetrically derived
from the original theological choice.
The analytical process begins with the acknowledgement that natural
law forms a dynamic system for both behavior and evolving knowledge
and technology. Within that closed system behavioral options can then
be stochastically determined.
2. Basic Mapping and META Game Theory
The introduction illustrated that George Washington Carver's strategy
was to comply with known natural laws. His needs were achieved by meeting
the needs of others from a First World nation-state. He had faith that
this result would be his highest eternal payoff. On the other hand,
the terrorist's noncompliance with known natural law is evidenced
by their lack of technological inventiveness. They meet their needs
by harming others from their Third World nation-states. They, too,
have faith that their behavior will result in the highest eternal payoff.
The objective of sustainable development is for assets to be used more
efficiently in our entropic universe, which includes man's evolving
in knowledge and technology. One could conclude that people who share
Carver's strategic behavior and payoff faith are more congruous to
this effort than are those people who share the terrorist's strategic
behavior and payoff faith.
Mapping the topography of such strategies and payoffs must first
incorporate the theological, T1, belief in an infinite God, causing one
to have the goal of complying with all known natural laws or not—a
T2 belief with less compliance or a T3 belief with the least compliance
beyond which physical death results. This point is represented by the
y axis, where the T1, the highest possible degree of human compliance
with known natural law, occupies the lower area of the I quadrant for
tracking present behavior and the II quadrant for tracking past behavior
using a larger time gradient. The T2 occupies the highest area in
quadrant IV, and T3 follows that area, becoming the lowest survivable
noncompliance with natural laws. Their historical behavior is recorded
in the respective areas of quadrant III.
Next, the time-in-relation-to-need levels sequentially occupy the x axis.
Last, intellectual ability, I is plotted on the z plane. The plot point
on the xy plane is linearly joined with the plot on the z plane in either
quadrant as it corresponds to the T belief. This connection of xy and
z points implies interpolation to make a smooth surface. That surface
usually creates arcs within the linear area of the T boundary of behavior,
which form waves. The complete area of the function, to the point
of physical death, indicates the potential for support of sustainable
development by complying with natural law. But the immediate area of the
function within the T zone suggests probable behavior by demonstrating
the past degree of compliance with natural law.
This three-dimensional, anthropological mapping process in socio-natural
systems outlines the holonomic META game. META game theory includes
all other game theories and simply means the Manifold Equation of
Theological Asymmetry. Contrary to the antiquated Prisoner's Dilemma
scenario commonly used, multidimensional information is compiled and not
oriented toward another player but toward the cooperation or defection
with the anchor of natural law. Individual maps can then be compared
with other players for analysis of likely behavior based on the T belief.
Latent semantic analysis is useful to linguistically identify correlating
eschatological evidence of the core T belief. Fuzzy analysis is necessary
to compare most, many, and least compliance with natural laws.
3. Mapping Individual Behavior
3.1 Dynamic (Macro) Model
All individuals can be thought of as homogeneous agents. Each has
identical and nonevolving need levels, senses, knowledge, and
decision-making processes. However, the input is calibrated by their
respective rationality, R, category, causing behavioral output consistent
with a general dynamic model of a T1 choice producing B1 behavior,
T2 producing B2, and T3 producing B3 track.
This dynamic or macro view has immutable bounds that ultimately confine
all human behavioral possibilities. The uniqueness of each person's
behavior lies in the chosen theological belief that provides the
authority/standard for rationalizing all input, which then produces
predictable action and reaction in the achievement of the hierarchical
common needs of survival, B1, economic security, B2, love and affection,
B3, status and self-esteem, B4, and self-actualization, B5. The T1 track
produces B11, B12, B13, B14, and B15 behavior. The T2 track produces B21,
B22, B23, B24, and B25. T3 produces B31, B32, B33, B34, and B35.
The quantifying of innate ability is a problem-solving capability.
People who are able to meet their needs fall into three categories: the
gifted, who invent complex tools; the average, who can't invent complex
tools but can use them; and the below average, who need supervision to
use complex tools.
A macro model has a y axis to plot one of the three theologies chosen.
The x axis plots the same five need levels of either the B1, B2, or
B3 track along the theological course, as they are achieved, by a time
gradient of years or generations. A generation is the time an average
person can become sufficient in meeting his or her needs, usually 20
years of age. The z plane plots the problem-solving or intelligence
level, I as either below average, lo, average, av, or gifted, gi.
This point is connected to the coordinate on the xy plane.
An example could be the data of (x, B11 at 15), (y, T-1), and (z, gi at
160 IQ), indicating a chosen T1 theology, that the survival need level was met
at 15 years of age, and the problem-solving capability of inventing
complex tools. The area of the function is T1 to possible T2 behavioral
compliance with natural law, which would indicate a positive response
to support sustainable development. It also implies an intellectual
potential to increase both the knowledge and the technology levels
A second plot is made when the second need level, economic security,
is achieved. It might be (x, B12 at 32), (y, T+2), and (z, gi at
160 IQ). The z number is unlikely to increase or decrease measurably
under normal conditions. Those plots are joined by interpolation
to the points first plotted. The third plot is made when the third
need level, love and affection, is achieved, etc. If it were (x,
B13 at 38), (y, T-1), and (z, gi at 160 IQ), this shows an arc, Barc,
back to the T-1 area, which is the equilibrium of the T1 theological
belief. This trend would be expected for each T belief unless there
is a conversion to a higher T belief. Otherwise, the potential is
the area of the function of each T belief. This general area of
decision-making strategy contains the potential of cooperation with
or defection from natural laws that can be compared with the maps
of others for an analysis of cooperation or defection strategies.
3.2 Stochastic (Micro) Model
A stochastic view records the micro decisions that are made within a
dynamic (macro) model. These decisions are expressed in probabilities
and imply that more information for mapping is required and available
than that of the previously covered dynamic model.
The II and III quadrants of the xy plane are for plotting the history of
need achievement in the same fashion as in the dynamic model. The I and
IV quadrants of the xy plane are for plotting the subsets of need level
decision making in days, weeks, or months. The y axis would reflect
the T level, and the I and IV quadrants of the z plane would reflect
the problem solving as seen in the dynamic model.
If one desires to map the individual from the dynamic model, the same
data would be plotted as follows:
x: -38, -23, -6
y: 1, -1, 1
z: 160, 160, 160
This information shows that this individual was born 38 years ago and
achieved the survival need B1 at 15 and the economic security need at 32.
It indicates a Barc from a T1 belief and a gi I level.
Stochastic or micro plots can now be added. For example, the data of
(x, B2 behavior at 1 month), (y, T-1), and (z, 160); (x, B2 behavior at
2 months), (y, T+2) and (z, 160); (x, B2 behavior at 3 months), (y, T-1)
and (z, 160) could be plotted as follows:
x: 1, 2, 3
y: 1, -1, 1
z: 160, 160, 160
This indicates the 38-year-old is attempting to achieve B13, love and
affection. The behavior reflects a formal long- and short-term strategy
Barc or waves from a T-1 to a T+2 compliance with natural law. If more
information was available, the stimulus that caused the arcs could be
identified as plots made in times less than a month. The graph time
gradients need only be expanded to accommodate the time subsets.
The Barc highs and lows of the area of the function can be extended
to indicate cooperation or defection with specific natural law by
probable occurrence, O, expressed as O1, 90% certainty; O2, 75% to 89%
certainty; and O3, 50% to 74% certainty. This map can also be compared
with stochastic maps of other individuals for analysis.
4. Mapping Societal Behavior
4.1 Dynamic (Macro) Model
Polarization of individuals with the same T beliefs will occur
to promote effort efficiency and lessen cognitive dissonance
that results when one is faced with inconsistent rationalities.
They will comprise three demographic groups from either a T1, T2,
or T3 belief system. Those with 51% or more are the P1 group.
The near majority of >24% but less than 49% make up the P2 group.
The least significant P3 group numbers between 2% and <24%.
Those groups influence the society's or nation-state's four
nonevolving institutions of family, Fa, church, Ch, business, Bu, and
government, Go. These institutions are composed of individuals who act
as homogeneous agents in a multiagent scenario or socio-natural system.
The subsets of the institutions from the R variable and T belief that
comprise the P1, P2, and P3 groups of individual behavior--B1, B2,
and B3--can be assigned demographically based on corresponding common
societal behavioral levels. The immutable and dynamic societal levels
create either First, 1W, Second, 2W, or Third, 3W, World political
systems/cycles. Just as in individual mapping, the difference in innate
problem-solving ability, I, plays a critical role in determining the
potential of decision-making behavior. Additional factors such as average
productivity, A, or the trust quotient, Q, will be affected.
A macro model of a First World, 1W, system has all five societal levels
based on corresponding individual need levels plotted on the x axis
as they are achieved or recalibrated as a result of crisis in years or
generations. The y axis plots the P1 theology of T1 in the survival,
1W1, and economic security, 1W2, levels. A paradigm shift from a
T1 to a T2 occurs between the P1 and P2 groups. The plot track will
fall from a T1 to a T2 track for the love and affection, 1W3, level.
Again, a shift occurs; this time the P2 and P3 change from T1 and T3
to T3 and T1, respectively. The last level, self-actualization, 1W5,
has a final shift to a P1 of T3, a P2 of T2, and a P3 of T1. This lack
of compliance with natural law signals the end of the 1W nation-state
cycle and the ergodic transition, ST, into either a new rational, STr,
1W1, or an irrational, STir, 2W1, or a 3W1 system/cycle. The z plane
plots by thousands, millions, or billions the intelligence level, I,
as either a I1 (85% to 90% av, 5% to 7 1/2 % gi, 5% to 7 1/2 % lo), I2 (<85%
av, >7 1/2 % gi, <5% lo), or I3 (<85% av, <5% gi, >7 1/2 % lo)
The Second World, 2W, system's y axis of a 2W1 level has a P1 of T2,
P2 of T3, and a P3 of T1. A shift occurs in the P1 to a T3 and the
P2 to T2 for the next 2W2 level. The 2W3, 2W4, and 2W5 levels are not
collectively achievable because of noncompliance with natural law and
another 1W1, 2W1, or 3W1 level is begun. The x axis and z plane use
the same increments as in the 1W model. Average tolerance to persistent
stress, S, is different between T categories of belief and thus will be
the time expected between levels. The stress of T1 is 15 to 30 years,
S1, T2 is 7 1/2 years to 15 years, S2, and T3 is 3 1/2 to 7 1/2 years.
Plotted on the y axis, a Third World, 3W, system has a P1 of T3, a P2
of T2, and a P3 of T1 and is therefore unable to attain the 3W2, 3W3,
3W4, or 3W5 levels because of the rejection of natural law. The x axis
and z plane may use the measurements as in the 1W and 2W models.
The direction of the area of the function in each map indicates the
potential to generally cooperate with or defect from natural laws that are
necessary for sustainable development. Specific models can be compared
with others for the prioritization of assets.
4.2 Stochastic (Micro) Model
Like the stochastic mapping of individuals, the societal micro model
requires more information than does the dynamic model. The II and III
quadrants of the xy plane plot the history of the achievement of societal
need levels as on the macro map which could include more than one cycle.
The I and IV quadrants of the xy plane are for plotting the subsets
of need level decision-making in days, weeks, or months. The I and IV
quadrants of the z plane gradients of measurement remain unchanged.
The arc, Warc, will form waves that create a direction of the area
of the function that is to be used to predict probable cooperation or
defection with specific natural laws. This precise model is also helpful
when making specific behavioral comparisons between nation-states Warc
momentum levels of certainty, O1, 90%; O2, 75% to 89%; and O3, 50% to 74%.
5. Mapping Global Behavior
5.1 Dynamic (Macro) Model
The collection of nation-states or complex adaptive systems can be
viewed in our global socio-natural system as homogeneous agents
in a multiagent scenario. They are made up of individuals who
form P1, P2, and P3 groups within the same four institutions that
create either First, Second, or Third World nation-state behavior.
Unlike solitons, nation-state collisions or warfare might not result
in the participants' keeping their W shapes/systems.
To consider the societies of the world as fuzzy fractals might be helpful.
They are self-similar in that each can be broken down into the same
smaller components of unchanging societal and individual need levels.
They can be roughly considered also to have an appropriate fractional
On a macro level, the hierarchical societal needs would be plotted by
years or generations on the x axis. The y axis would plot the total 1W,
2W, and 3W systems. The z plane would plot by billions the I level.
An extension of the area of the function would indicate the global
potential for sustainable development in this dynamic system.
5.2 Stochastic (Micro) Model
As more global information is collated, a micro model can be
created that indirectly produces stochastically decision-making
probabilities. The y axis continues to track the T levels and
the z plane the I level by population totals. The x axis plots
the total P1, P2, and P3 groups without regard to geographic
borders. Traditional nation-state boundaries have been made less
relevant as a result of technological advances in communications
and transportation. Today, individual cooperation and defection
strategies are less aligned with national identity than those with
the same T beliefs. This situation is naturally precipitating a
noticeable global polarization of T categories. The arc, GLarc,
can be used to predict the probability of global compliance with
A method of prioritizing the distribution of finite resources has
been presented to answer the decision-making questions posed in the
introduction of why George Washington Carver had the freedoms and
ability to create more efficient use of farm products and land with
meager means and conversely why wealthy terrorists do not create
but attempt to destroy the efforts and lives of people like Carver.
The individual Theological choice creates the epistemological
authority/standard for Rationality that provides the motive for the
behavior in pursuing common Individual needs. Like-minded individuals
form groups that cause Collective behavior based on the
faith of the original theological belief—TRICE.
When META game theory is displayed graphically in xy and z planes, the
area of the function can provide both dynamic (macro) and stochastic
(micro) evidence of the potential strategies of cooperating with or
defecting from the parameters of natural law based on the perceived
theological/eschatological payoffs. In this learning domain lies the
essence of socio-natural systems where (co-) evolutionary processes such
as knowledge and technology can be studied deontologically. Inventions
and discoveries such as dichloro-diphenyl-trichloro-ethane DDT can be seen
to require increasing intellect and knowledge of natural law to implement,
especially those designed for use in hostile environments such as the
ocean floor or the moon's surface. It seems paradoxical that although
these increases require more compliance with natural law, historically
T levels will decrease. Actually, inventions are anthropological tools
to meet needs and are thus expressions or self-creations that expose
the true motives of compliance or defection with natural laws to which
the majority will choose the latter course. Widespread resistance can
be expected to new ideas, but if they are proven useful, as in airplane
flight, they will eventually be accepted by the populace. Although a
part of nature, creations such as dams--which may be formed by a mud
slide, beavers, or man--each becomes a component of our socio-natural
system but do not have resilience. Their equilibrium is to return to
their natural state as dams eventually fill with silt and deteriorate.
To create with the capability to absorb, utilize, or even benefit from
perturbation and changes without a qualitative change in the system
structure and return to equilibrium requires infinite knowledge and
In conclusion, the increases in anthropological mapping ability should
allow public administrators to apply confidently regional and global
policies that sustain man and this terrestrial environment.
The author appreciates the pioneering efforts of John Nash at
Princeton University for static game theory, Leon Petrosjan at
St. Petersburg University for dynamic game theory, David Yeung at
Hong Kong Baptist University for stochastic game theory, and the
legacy of epistemological methods by George Washington Carver.
Adair, Gene. George Washington Carver: Botanist. New York: Chelsea House;
Area Handbook Series. 101 volumes. American University
Bell, Dallas F., Jr. How Theology Dictates Political Systems. Paper
presented at the theological conference at Mid-American Baptist
Seminary. 2002; Memphis, TN
Bell, Dallas F., Jr. The Primary and Secondary Precursors to Mathematical
Formulations in Dynamic Games. Paper presented at the New Economic
Windows conference at the University of Salerno. 2004; Salerno, IT
Bell, Dallas F., Jr. The TRICE Lecture. 2004
Casebook On Insurgency. volumes I and II. American Military University
--ALL RIGHTS RESERVED (2005) Dallas F. Bell, Jr.--