Dynamics of human behavior

Wikipedia:Nash_equilibrium: John Nash's Non-cooperative game theory

Preprints

Douglas R. White Dynamics of human behavior MBS

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Background

"Dynamics of Human Behavior," is a 22pp entry (review article) by Douglas R. White for the Encyclopedia of Complexity and Systems Science. Heidelberg: Springer DE. submitted for publication (c) Douglas R. White under Creative Commons citation copyright. IMBS Working Paper 08-03

This remainder of this file should only be regarded as reading notes and provisional ideas, many of which do not appear in the completed manuscript.

Glossary

components, or fundamental variables of a system, may be various types of units or spins. Components may be composed of more of the self-same components at one goes to shorter distances or lower scale. See: fractal. A system will generally make self-similar copies, with slightly different parameters describing components and their interactions.

parameters of a theory typically describe the interactions of the components. These may be unit parameters or "coupling constants" that measure the strength of various forces.

fractal: a pattern or object (e.g. geometrical) whose parts echo the whole, only scaled down, i.e. scale invariant; invariant at any scale of magnification or reduction. “To improve almost any fractal model it is a good idea to replace it with a multifractal one” (Mandelbrot 2004:209).

multifractal (root and generator): a composite pattern that begins with an initial root (e.g., a straight line) that is successively replaced with a generator (e.g., a zagged line) that replaces every instance of the initial element. See fractal, power law.

power law: “multifractals have tails that follow a power law” (Mandelbrot 2004:209) in how the frequency of similar units at different scales varies with the scale; see multifractal. Note that power laws tend to become ubiquitous when what is studied involved dimensional constraints.

renormalization: a mathematical apparatus that allows one to investigate the changes of a pattern or system viewed at different (e.g. distance) scales. renormalized reduction allows successive changes of different patterns to be compared insofar as their successive reductions converge; and may be the reverse of multifractal generation. Renormalization is related to scale invariance, and the symmetries by which a system appears roughly the same at all scales, with changes in detail at smaller scales taken into account by renormalization “group” equations.

sufficient statistic: Let X1, … , XM/ be a random sample, governed by the density or probability mass function f(x|θ)/. The statistic T(x) is sufficient for θ if the conditional distribution of x, given T(x)=t, is independent of θ. Equivalently, the functional form of fθ|x</(x) does not involve θ, and The Fisher-Neyman Factorization Theorem may be used to help spot sufficient statistics. The Likelihood Ratio Test can often be reduced to a sufficient statistic of the data for hypothesis testing. The Minimum Variance Unbiased Estimator of a parameter θ can be characterized in parameter estimation by sufficient statistics and the Rao-Blackwell Theorem. See Scharf L (1991) Statistical Signal Processing. Addison-Wesley. A sufficient unit is one for which a random sample of aggregate statistics are sufficient.

I. Definition of the Subject and Its Importance

```(Concise definition of the subject and its importance with brief historical background)
```

Dynamics of Human Behavior overlaps with Human Social Dynamics (abbreviated, DHB, HB, HSD). HB dynamics are concerned with the effects of causal forces on changes in humans and social objects, their movements and behavior. Such dynamics are distinct from kinematics, which describes movement and change in behavior without considering causes, while movement and change distinguishes them from statics. Social statics and comparative studies of human behavior and complexity consider stable distributional properties of social objects or systems. Social dynamics may refer to spatial and temporal local interactions, changes in distributional properties, and synchronous or asynchronous dynamical evolution for different levels of social entities. DHB takes into account the distinctive behaviors of humans and the range of their sociopsychocultural differences, in contrast to the more generic human dynamics, including robotics, in which movements and actions of humans are simulated, but these may also be complex, as with models of gait. People are complex entities (formed of component sub-entities) that form composites on a larger (multi-person) scale where behavior of entities subsumes constituent members. The interactions between individual behaviors and those of institutions, organizations, and roles, or within legal or informal normative constraints are part of the phenomena of DHB to be explained. DHB precursors include Ibn-Khaldun’s 14th C. characterization of the cycles of oscillations of Muslim political dynasties as between military regimes with limited pluralism and more intolerant fundamentalisms, with decadent urban elites replaced by charismatic tribal initiatives that devolve into decadent urban elites, and concomitant oscillations in how social cohesion is distributed. Richardson’s (1960) pair of equations with their basins of attraction for stability, disarmament, or the arms race, were memorable behavioral dynamic models, as was Thomas Schelling’s "focal point" for "each person’s expectation of what the other expects him to expect to be expected to do" as a game theoretic solution in The Strategy of Conflict (1960), which pioneered the study of strategic behavior and bargaining.

II. Introduction

Fundamental problems of DHB include (1) units of analysis, (2) interaction equations and structures, (3) levels of analysis, and (4) sufficient statistics. Given these problems, dynamics may refer to how forces are quantized, as in quantum electrodynamics or quantum chromodynamics. This does not extend to equating quantum or any other branch of physics with the human sciences, which seems to be the analogy of econophysics. Typically, the research strategies for a hierarchy of sciences are lateral, not a reductionism from one to another at a different level, but from some potentially common principles for all, with lateral applications reworked or finely tuned to different levels and problems. In this view, mathematics and principles used in physics could apply at any level in the scientific disciplines, but principles discovered in the human sciences might be found to apply more generally as well.

The logic of this article begins with problems concerned with the “units” of investigation as they are organized into systems, usually multifractally, even if only through reproduction, evolutionary phylogeny, and developmental ontology. As we move on to networks, however, in recognition of the lack of hard units and hard wiring in living systems, fluid- or hydrodynamics, nonlinear synchronization, percolation theory derived from the study of graphs and lattices, and generalizations of entropy measures may provide more useful material for testing lateral models borrowed from physics than mechanics, solid-state physics, or conventional entropies.

Formal approaches to DHB—where by formal is meant close investigation and characterization of phenomena prior to constructing models (Leaf 2007)—require construction on the basis of careful “descriptive,” qualitative, and quantitative research about human (including institutional, etcetera) behavior such as are carried out in the disciplines (history, sociology, economics, psychology, cognitive science, political science, linguistics, and anthropology, including ethnography, archaeology and other domains). The best-known formal approaches in the complexity sciences are “sufficient unit” equation modeling, network modeling, and simulation modeling (equation or agent-based, or both). Less well known are experimentation, which is especially strong in network economics. Fractal dynamics has played a different role in economics, where it has challenged fundamental axioms, say, of market systems. We might assume that which many principles of complexity sciences will apply to many disciplines, how they apply in detail will vary with subject matter.

Unlike scientific models that begin from principles of independent interacting units—the gas laws or those of nonelastic solids (where F=MA applies to bodies whose interiors are not considered and whose motions are independent except for collisions), and where entropy is considered to be Boltzmann-Gibbs under the assumption of statistical independence, the fractal, “sufficient unit,” and network approaches to studying HSD and DHB begin with assumptions of quasi-independence. Fractals start with the notion that “units” of behavior in time-series compress memory and repetition of structure, and interactions are not dependent on scale. “Sufficient unit” modeling looks for aggregates at particular scales that represent relative closures of systems in which internal dynamics can be studied for certain types of units that occur in limited ranges of scale. Network modeling finds means of bounding and measuring fields of interaction where particular kinds of units and their relations can be specified, and modeling assumes that those units and relations have some effects or constraints on interactions.

III. Multifractal dynamics, power laws, (social) turbulence, and hydrodynamics

From within a social science perspective, it may seem odd that the study of scale-invariance, so common in physics, and which connects multifractal dynamics with power laws, should erupt into the kinds of turbulence that is studied in hydrodynamics. When physicists site down with social scientists to discuss modeling, early conversations range from how the latter are so fascinated with Pareto laws, such as those of income distribution, and which seem to have a “stable” condition that normalizes class division, while the former (physicists) typically study power laws as they converge on the very small or the very large where disruption and phase transition occurs. Mandelbrot’s work in the mathematics of markets, initially puzzling to economists, provides the best discussion about how these two seemingly irreconcilable conceptions of invariance can coincide. The convergence of these two frameworks—stabilities and instabilities—is also beautifully exemplified in the work of Santa Fe Institute groups working on biological, ecological, and social scaling. Misunderstandings are partly due to how things look through opposite ends of multiple spectroscopes.

Mandelbrot (1963:405, 2004:163) shows that daily and changes in cotton prices for the USA, for various periods from 1900-1958, both up and down, followed a stable Paretian law with δ = 0, α = 1.7 and β = 0, with the various graphs as horizontal translates of each other, and not Gaussian as predicted Brownian movement of market price hypothesized by Bachelier (1900) that had become the standard assumption in economics. Figure 1 Mandelbrot (1963:91) shows a similar pattern for the Dow, 1915-2000, with log(prices) and log(price changes) in the upper and lower graphs. Crashes in the 1929-1932 period, for example, are log scale invariants in terms of their magnitudes. He shows how to imitate the kinds of changes in the upper left curve with multifractals (lower left). Volatilities of the 1900-2000 stock prices are shown monthly (2004:112-113) in the upper right of Figure 1. The lower right (2004:94) compares a standard Bachelier standard deviation σ measurement of these volatilities (in gray) ranked by size (no changes greater than 5σ) to fractal variants (in gray) with many σ>5 values at one at 24σ, the collapse of 1929. Whether the σ2 variance is infinite rather than finite depends on whether α>2 (it was 1.7 for cotton prices). Nobelists Robert F. Engle (NYU) and Clive Granger (UCSD) won the 2003 economics prize for defining the spectral shape of the stock market multifractals.

Mandelbrot argues that value is not a useful concept in economics because while volatility is predictable value and direction are not. Daniel Kahneman (2003 Maps of bounded rationality: A perspective on intuitive judgment and choice. In T. Frangsmyr (Ed.), Les Prix Nobel 2002 [Nobel Prizes 2002]. Stockholm, Sweden: Almquist & Wiksell International.), working with Tversky, extended this view to the lack of empirical evidence, given that experimental studies show reference-dependent framing of judgments, for the value of expected utility theory as originally framed by Bernoulli (1738) in reference-independent terms. Farmer, Patelli, and Zovko (2005) concur by showing that zero-intelligence market strategies do as well in outcome distributions by success as actual distributions. There is no characteristic scale in that levels of success are frequency-distributed as power laws, like Pareto’s (1896) income distributions, or Zipf’s (1949) word frequencies. Multifractal dynamics occur in the human heartbeat signal interval and the fractal-gait organization of human walking that has been discovered in robotics. For psychophysics Steingrimsson and Luce (2005a,b,2006,2007) find that perceptions of intensity to track only the physical ratio of the signal to the reference signal by a psychophysical power function, except for numerals, for which a minority of people in experiments tend to overweight small probabilities and underweight large probabilities following a general Prelec (1998) function. It is notable that psychophysics is not to the point where very specific functions can be identified for sets of subjects. In this case, the gamblers’ Prospect theory (Kahneman and Tversky 1979) for decisions under risk is one of several models that would explain minority decision rules for discounting low probabilities. Brain scans applied to studies of political cognition through fMRI have led to strong evidence that establish differences in political behavior between political sophisticates and political novices that arise from their use of different neural substrates. The research design is aimed at a model of the emergence of ideology, unifying insights from work on neuropolitics with my agent-based models of party dynamics. The hypothesis is that ideology is an emergent feature of competition among political actors who alter the space of political debate and are then constrained by the resulting alterations (website of UCSD political scientist Darren Schreiber).

Evolutionary dynamics add an extra dimension. In branching evolution, diversity increases with branching and separation. Many human languages display phylogenetic trees (Tanmoy Bhattacharya, using software described in Science 2000) that show branchings for large macro-phyla in a range from 12-8,000 years BP, roughly corresponding to independent human groups that survived into the neolithic. Further branchings tend to slow linguistic a copies of “same” languages tend to replicate, whether through migration or takeovers by successful or dominant languages. Analysis of word changes in English (Old-Middle-Modern) by Lieberman E et al. (2007) show a regularization rate per verb that varies by the Zipfian power law = 1/f frequency, while irregular verbs have exponential decay over this period, where the half life of an irregular verb is a constant interval of time (we won’t be saying “happily wed” much longer, but “wedded” as we is on the danger list). Led by Geoff West at SFI, groups of researchers in biology, ecology, and the social sciences begin with a view that the multifractal dynamics organize the “space filling” branching transport systems of organisms, and that it is the branching and filling parameters (e.g., a ubiquitous ¾ power law found most basically in mass to metabolism relations across species) from which the organizing biological relationships from for ontogeny to ecology, explaining the host of allometric relationships found in all these areas. This overarching multiscaling theory accounts for efficient energetic optima found in species and ecologies. In the socioeconomic realm, such as cities and their resource distribution systems, many such optima are found, but not in the organization of export production and knowledge systems. The idea here is that cities must grow to complete with other cities fueling their growth by returns to market exchange, and the requirements for competitive growth push the growth parameters beyond the level of increasing returns to scale, resulting in instabilities that are not present in ¾ and derived power laws in biology.

This sort of instability has two aspects—static and dynamic, described in Bettencourt et al. (2007). Dynamically, the supercritical rates of recruitment of talented inhabitants that can help their productive economic growth and competition—ones that cities require for their survival in that failure leads to their demise—drains inhabitants from rural areas (who are then free to reproduce) while disproportional growth rates in cities increase both the urban/rural ratio (and percent urbanization) and the global population. These ratios also produce world population growth that has an unsustainable power law upturn that if continued as a mathematical curve would result in infinite population within a relatively short interval of time, resulting in population crises both locally and globally.

Meanwhile, at the movies—Art De Vany and David Walls (2001) show that in the USA: 1) box-office revenues of movies without stars are Pareto-distributed with finite variance, 2) box-office revenues of movies with stars are Pareto-distributed with infinite variance, and 3) growth in the first distributions is stochastically dominated by the second. There is no characteristic scale to blockbuster movies, and no predictability as to profits once stars are introduced. The next blockbuster profits can be nearly any multiple of the last, just as the success level of any city that dominates its markets can be nearly any multiple of the last. This is what Barabási (200*) has characterized dynamically as leading to winner-takes-all systems. If we consider that winner-takes-all is unsustainable, that its correlate is global impoverization, and that the resources engaged in urban and entertainment potlatching are actually be dissipated into global warming and unsustainable climatic conditions for humans, we can say, like those physicists studying criticality (i.e. unsustainablity) in transitions governed by power laws, that human systems on a planetary scale are approaching criticality.

“Diverse systems with the same critical exponents—that is, which display identical scaling behavior as they approach criticality—can be shown, via renormalization group theory, to share the same fundamental dynamics.” — Wikipedia (Power law). Note that if it is the critical value of the exponents here that has those effect, is there subcritical power-law growth? Yes: stable population growth or power law population decline, such as Pt Pt-1α where α ≤ 1. But that doesn’t happen without a change in the ecology of cities. We will encounter this question again under networks – e.g., scale-free network navigabilities in the 2 ≤ α ≤ 2.4 range (Adamic, Lukose, Huberman 2003).

IV. Experiments

Experiments involving humans are used in network economics to validate or refute fundamental assumptions about conditions for convergence or nonconvergence to equilibrium in markets. Unlike physical experiments, they lack sufficient controls for the sociopsychocultural makeup of subjects. In those pioneered by Charles Plott, that have diffused widely in economic research groups, significant amounts of money are other payoffs are used to test theories about economic maximization. Field experiments for classical decision problems are now widely carried out across cultures (Joseph Henrich, together with Samuel Bowles and others at SFI), and complemented by those carried out concurrent with brain scans (e.g., Darren Schreiber) that convey direct knowledge about cognition.

Of special interest are those network economic studies that model within the experiment elements identified from ethnographic and historical contexts to have had probable impact on evolutionary trajectories. Drawing from Avner Greif’s (1997) intensive historical study of institutions that facilitate impersonal exchange in pre-modern Europe http://www-econ.stanford.edu/faculty/workp/swp97016.pdf that then maps the historical processes into appropriate game theoretic models for experimental studies. Kimbrough, Smith, Wilson (2006:1) then explore in well-designed laboratory experiments the conditions for emergence of impersonal markets.

Greif (1993, 2006) reconstructs two specific lost histories of community-based systems of responsibility that supported impersonal exchange in medieval Europe and that laid the foundation for broader, law-based systems to eventually supplant them. Using the experimental method, this paper attempts to complementarily reconstruct our understanding of such transitions by directly observing how Adam Smith’s natural propensity expresses itself as cash-motivated participants discover and implement local and distal exchange networks in the laboratory.

Kimbrough et al.'s previous work (CWS) showed that a small majority of subjects

```either immediately settle into autarky or start to specialize in the good in which they
have a comparative advantage. The rest typically follow an erratic development over
time, in which most trade occurs between appropriately specialized subjects with
complementary comparative advantages. By the end of the experiment, half of the six
two-person economies find and achieve the welfare maximizing competitive equilibrium.
What is extraordinary is that once they discover exchange, they almost immediately
discover the competitive equilibrium price. Moreover, the language of discovery is not
that of “bargaining” and “price,” but mutual sharing of information in learning what
constitutes their combined interest, and the language of exchange highlights reciprocal
in which they tend to achieve efficient home production, but fail to discover the far
more efficient specialization and exchange equilibrium with another person.
```
```[We concluded] that there are three interrelated stages in learning to achieve the
competitive equilibrium in these economies: (1) discovering the ability to exchange,
which may require “mind-reading” (inferring intentions from words and actions) and
imitation, (2) finding a suitably endowed partner with whom a subject can discover
the benefits to exchange through specialization, and (3) building the relationship
by increasing specialization over time. However, in these model economies, no market,
as it is commonly conceived, ever emerges. People either do not exchange or remain
firmly entrenched in bilateral personal exchanges that are not characterized by the
language typical of “bargaining” as we normally model it. One quotation from CSW’s
transcripts summarizes the personal cooperative disposition of the agents: “I’m
trying to think how maybe we could help each other”. Even more intriguingly, in the
eight person treatment, where folk wisdom would most strongly predict the creation
of a market, the level of exchange and specialization observed is at a relative minimum.
```

In redesigning the experiment

```we first allow the subjects to explore two-, four- and eight-person communities in
sequence, then we introduce long-distance trade and a third commodity after this
experience.
The question remains. Under what conditions will we observe the emergence of impersonal
exchange out of the highly personal exchange that CSW found to  characterize this
institutionally sparse environment? With this new experiment we aim to create that second
sphere of interaction by introducing new possibilities for the development of impersonal,
market-like exchange. Specifically, we introduce opportunities for distal trade to emerge
between three CSW economies. By also introducing a third good and the ability for a
subset of the participants to travel between villages, we provide ample opportunity for
our subjects to set up more complex networks of exchange in order for us to better
understand the transition from the personal to the impersonal.
```
```Unlike historical investigations, in the laboratory we have the ability to induce
different institutional histories on our economies and then observe how these different
points of origin affect the developmental trajectories of the more complex economies
studied here. North (2005) argues that belief systems and the stock of local knowledge,
the internal representations of the human experience, are intimately intertwined with the
external institutions that humans build. We investigate this relationship by varying the
degree to which property rights are enforced in yesterday’s institutions before the
opportunities for long-distance trade present themselves with perfectly enforced property
rights. Specifically, in the new experiment we report here, three-fourths of the subjects
in an economy are drawn from two different treatment histories in Build8 sessions, one in
which property rights in personal goods are perfectly enforced for all of the
participants, though they must rely on trust and repeat interactions to enforce exchange
agreements, and another in which no property rights of any kind are enforced. Hence, in
both sets of history-inducing sessions, there is no external enforcement of exchange
contracts and, as found by CSW, no need for such.
```

Their findings: “We find that a history of un-enforced property rights hinders our subjects’ ability to develop the requisite personal social arrangements necessary to support specialization and effectively exploit impersonal long-distance trade.” Thus we might understand through network economic experiments the origin of the market system to which Mandelbrot has assigned unpredictability, hence turbulence, and to which the city–economies scaled by Bettencourt et al. (2007) have assigned inefficient and unnecessary growth and I and others, in examining both population pressure and anthropic climate change have assigned unsustainability.

V. The (agent-based) “network” (formal) modeling approach

This approach disaggregates to the relatively autonomous units—like individuals or corporations—that interact in a discrete pairwise manner or in higher order groupings and contexts and to attempt to explain behavioral dynamics in terms of causal-emergent relationships (tipping points, etc.) between micro, middle, and macro-level properties of units and interactions. Roughly speaking again, complexity in the “network” modeling approach requires taking into account how the reaction times of component individuals or their groupings in the network compare (and exhibit complex memories with a temporal spectroscopy) with the pairwise transaction times and their spectroscopies.

Emily Erikson, Amherst, and Peter Bearman, Columbia, Dynamics of East Indian Company Trade Malfeasance and the Foundations for Global Trade The Structure of English Trade in the East Indies, 1601-1833 American Journal of Sociology 111:6.
STRUCTURALLY COHESIVE SCALABILITY
THE EVOLUTION OF COOPERATION

(ALL TEXT BELOW IS PROVISIONAL IF NOT COMPLETELY OBSOLETE)

A review topic such as human behavior covers very large literatures in many different fields. The focus of this review is on topics that would engage salient interests about the human history, society, and knowledge about dynamics that might positively affect our future prospects. The idea here is not to address humans outside of their social contexts or that address how to manipulate human beings, to create robots to replace human beings, to design the control panels of weapons for use against human beings, as some of my colleagues have egregiously done. The study of human dynamics might better serve the goals of human existence rather than misguided ideas about the means to those ends. By looking at issues of human behavior in the contexts which which the majority of people live studies of dynamics can address the large questions such as the feedback between our behavior and anthropic climate change, the effects of the built environment, that between humans behavior, population, resources, resource distribution, scarcity, and warfare, and a host of other topics where dynamics becomes crucial for our understanding of the interaction between social, behavioral and earth processes.

(As I am only beginning to write), This review begins by considering the dynamical interaction between

1. human behavior, the built environment, overcrowding and congestion, and a host of modern problems related to industrial society and its impacts, focusing primarily on historical and future transport systems, energy efficiencies, population and environmental degradation, the problems of the ecological commons, etcetera.
2. human behavior, the social environment, overpopulation and competition, and the problems of internal and external warfare.
3. human behavior, the evolution of cooperation, and variable of network cohesion.
4. human behavior, the urban environment, the pace of city life, and the problems of the economy.

Dynamics of human behavior and the social environment

.....Dynamics of Bands, Chiefdoms

An Evolutionary Agent-Based Model of Pre-State Warfare Patterns: Cross-Cultural Tests Mikhail S. Burtsev and Andrej Korotayev, 2004 World Cultures 15:17-38.

.....Dynamics of border conflicts

Turchin's Historical Dynamics: Disequilibrium and external war
responsive cohesion
Carneiro's circumscription theory

.....Dynamics of Cohesion--> Response to threat--> Nations

why interrogation doesn't work (Battle of Algiers)

.....Dynamics of Hierarchy--> Bicomponents to tricomponents

Overcoming segmentary (chiefdom) organization --> states

.....Political Dynamics

Lars-Erik Cederman Emergent Polarity model of early nation-state geopolitics (1997, 2002)

Cederman, Lars-Erik, 1997, Emergent Actors in World Politics, How States and Nations Develop and Dissolve, Princeton University Press, Princeton, NJ.

Cederman, Lars-Erik, 2002, Endogenizing geopolitical boundaries with agent-based modeling, Proceedings National Academy of Sciences, Vol 99, suppl.3: 7296-7303.

Dynamics of the Division of Labor

Xavier Ragot "Technical Change and the Dynamics of the Division of Labor" http://ideas.repec.org/p/del/abcdef/2003-09.html
Dynamics of the Sexual Division of Labor

.....Dynamics of Product Spaces and the Development of Nations

Hildago, C., B. Klinger, A.-L. Barabási, and R. Hausmann. 2007. The product space conditions the development of nations. Science 317(July 27):482-487. Abstract available at http://www.sciencemag.org/cgi/content/abstract/317/5837/482.
Supplemental information about the Product Space and the Wealth of Nations is available online at: http://www.nd.edu/~networks/productspace/index.htm.

.....Dynamics of internal fission

Turchin's Historical Dynamics: Scarcity and internal war
Axtell, Robert L., 2002, Population growth and collapse in a multiagent model of the Kayenta Anasazi in Long House Valley, Proceedings National Academy of Sciences, Vol 99, suppl.3:7275-7279.
Chiefly recycling - Marcus, Joyce, 1992, Dynamic cycles of Mesoamerican states. National Geographic Research & Exploration 8:392-411. National Geographic Society, Washington, DC.
Chiefly recycling - Read, Dwight W., 2002, A multitrajectory, competition model of emergent complexity in human social organization, Proceedings National Academy of Sciences, 99 suppl.3: 7251-7256.
Chiefly recycling - Arthur Griffin and Charles S. Stanish (2007) “An Agent-based Model of Prehistoric Settlement Patterns and Political Consolidation in the Lake Titicaca Basin of Peru and Bolivia”, Structure and Dynamics: eJournal of Anthropological and Related Sciences: Vol. 2: No. 2, Article 1.

Bandy, Matthew S., 2004a, Fissioning, scalar stress, and social evolution in early village societies. American Anthropologist 106(2):322-333.
Carneiro, Robert, 1970, A Theory of the Origin of the State, Science 169:733-738.
Earle, Timothy, 1997, How Chiefs Come to Power, Stanford University Press, Palo Alto.
Epstein, Joshua M. and Robert Axtell, 1996, Growing Artificial Societies, Social Science from the Bottom Up, Brookings Institution, Washington D.C and the MIT Press, Cambridge, MA.
Epstein, Joshua M., 2006, Generative Social Science: Studies in Agent-Based Computational Modeling, Princeton University Press, Princeton, NJ.
John H. Holland - Holland, John H., 1995, Hidden Order, How Adaptation Builds Complexity, Perseus Books, Cambridge, MA.
Bruce Trigger
Keeley, Lawrence H., 1996, War before Civilization, the Myth of the Peaceful Savage, Oxford University Press. Oxford, UK.
Kohler, Timothy A., et al., 1999, Be There Then: A Modeling Approach to Settlement Determinants and Spatial Efficiency Among Late Ancestral Pueblo Population of the Mesa Verde Region, U.S. Southwest, In Dynamics in Human And Primate Societies, Agent-Based Modeling of Social and Spatial Processes, Kohler, T A, Gumerman, G J (editors), Oxford University Press. Oxford, UK.
Kohler, Timothy A., G. J. Gumerman, and R. G. Reynolds, 2005, Simulating Ancient Societies, Scientific American 293(1):76-83.
Kohler, Timothy A., et al., 2007, Settlement Ecodynamics in the Prehispanic Central Mesa Verde Region, In The Model-Based Archaeology of Socionatural Systems, T.A. Kohler and S.E. van der Leeuw, eds., School for Advanced Research Press, Santa Fe, NM.
Schelling, Thomas C., 1978, Micromotives and Macrobehavior, WW Norton and Co. New York, NY.
Spencer, Charles S. 1993, Human agency, biased transmission, and the cultural evolution of chiefly authority. Journal of Anthropological Archaeology 12:41-74.
Wilkinson, Tony J., et al., 2007, Modeling Settlement Systems in a Dynamic Environment, Case Studies from Mesopotamia, In The Model-Based Archaeology of Socionatural Systems, T.A. Kohler and S.E. van der Leeuw, eds., School for Advanced Research Press, Santa Fe, NM.
Kuang, Yang A state-dependent delayed predator-prey model. AIMS' Fifth International Conference on Dynamical Systems and Differential Equations. (June 2004). https://sec.was.asu.edu/directory/person/11246 (he is writing the http://scholarpedia.org/article/Modern_Predator-Prey_Models for the Encyclopedia of Dynamical Systems
James Moody's thesis on the "balance theory" dynamics of friendship -- 5 best friend graphs, 1 for male, 1 for female

Dynamics of evolution of morals

.....Evolutionary Game Theory

Bryan Skyrms: Evolution of the Social Contract (1996) - Fairness in the ultimatum game (1); in the prisoners’ dilemmas-cooperative (2); divide-the-cake-just (3); etc (4); etc Meaning and Language (5).

(1) and (2) are irrational, if utility is measured in a certain way. (3) it is no more rational than other possible actions under the concept of Nash Equilibrium. etc. How might these inclinations have evolved under the pressure of natural selection? What explains our ethical intuitions?

Bill Harms has a simulator for the dynamics of some of the games in Evolution of the Social Contract: it can be found by clicking http://www.ethics.ubc.ca/eame/eameweb/Skyrms

Bryan Skyrms: The Stag Hunt and the Evolution of Social Structure (2003)

.....Dynamic Evolution of Rational Minimax Principles

Why classical minimax doesn't work

Dynamics of human behavior and the evolution of cooperation

The problem of cooperation
Defectors and the Tragedy of the Commons
Bruggeman's evolutionary dynamics
Legal enforcement with minimization of punishment

Dynamics of human behavior and the urban environment

The dynamics of growth: population and infrastructure (West et al.)
The dynamics of population instability

Dynamics of human behavior and aggression

One idea here is to look at aggression in network terms, as positive (cooperative) and negative (aggressive) relations. Bruggeman has an up-to-date discussion

Dynamics of human behavior and the built environment

Redesigning road systems for global sustainability

New Theorems and old, explained

Saari - why politics isn't rational Book in press: “Disposing Dictators; Demystifying Voting Paradoxes.” finished in late spring of 2007, probably will be published by Cambridge University Press. Multiscale analysis.
Donald Saari (with Jason Kronewetter: completed the first part of our analysis of a topological analysis of decision problems).

(with Ivy Li completed our analysis of Sen’s theorem).