This site is part of a project on Advanced Decision Theory that starts with the Theory of Games and extends it using deterministic techniques from differential geometry and physics. These techniques have proved useful in electrical engineering, meteorology and general relativity. The approach has much in common with the techniques of systems dynamics. Using tools of Computational Engineering, this approach provides insights into such diverse topics as the prisoner’s dilemma in game theory, ethical issues of the tragedy of the commons and current day strategic economic behaviors. The applications of such a theory extend to most common day experiences of decision-making. Anyone that is familiar with decision-making knows that it requires leadership, accountability, integrity and innovation. It is easy to make the prediction but hard to live with the results when they differ from the prediction.

This site will provide resources to understand and compute in the context of this generalization of game theory. Since the approach is not statistical, these resources may provide the necessary background to understand and work in this field. The resources consist of introductory materials, published materials, Wolfram Mathematica® notebooks, inquiries and white papers. Contributions from other authors are welcomed.

For a high level introduction, see the PowerPoint 2011 Wolfram Technology Conference Talk, a CDF talk Wolfram Technology Conference 2012 Talk, or the YouTube Video of that talk, which was given at the 2012 Wolfram Technology Conference held October 17-19, 2012. The presentation can be viewed using the free Wolfram CDF Reader. For a published introduction of decision process theory, see Geometry, Language and Strategy, Thomas, 2006, World Scientific (New York) and Geometry, Language and Strategy–Vol. 2 Dynamic Decision Processes, Thomas (World Scientific, 2016), which is a self-contained expansion of some of the white papers on “the dynamics” to be found on this site:


Advanced Decision Theory: this is an trans-disciplinary mix of ideas of geometry, language and strategy, starting with a causal foundation built from the language of differential geometry, using and implementing ideas such as gauge theory (Maxwell’s theory of electromagnetism, Einstein’s general theory of relativity, least action, geodesics, etc.), unification theories (such as Kaluza Klein, super symmetry, Higgs scalars, etc.), and the solution space associated with such theories such as harmonic wave phenomena (light waves, gravity waves, elastic vibrations); you will also find an  application domain foundation based on the game theory of Von Neumann and Morgenstern including the normal form for competitive and cooperative games, Nash equilibrium, open problems in the literature such as the prisoner’s dilemma, attack defense models, inequality models, the invisible hand (Adam Smith), tragedy of the commons, dynamic games and a critique of Bayesian probability; as the third component of the mix, you will find practical applications in the spirit of systems dynamic thinking to contemporary issues and related ideas, such as the early work of the Club of Rome (Meadows) and more recent ideas such as network science (Barabási).

This mix is synthesized into a single package called decision process theory, which I hope will both  educate and stimulate thought for a better understanding of decision processes. The presentations on this site are expected to range from philosophical discussions to presentations of exact solutions (to the field equations, which are analogous to those of general relativity) that illustrate this new way of looking at decisions. In the process of creating decision process theory, a number of distinctions were created with precise meanings and are defined and discussed in-depth on this site: causality, aggression and limits to greed, network connectivity, still point and free fall, harmonic standing waves, acceleration, code of conduct, entitlement, engagement, player interest, player passion, mutual player support, and strategies that are hidden-in-plain-sight.

SITE CONTENTS: The site is organized around five major areas. Three of them provide personal background on the author: About Me, Contact Me and Projects. The remaining two provide resources  for understanding decision process theory: Inquiry and White Papers. Mathematica notebooks will be found with the White Papers.

Recent Posts

Tyrant Model using Decision Process Theory

A classic game theory model for a tyrant might be a game of chicken, with a tyrant against the poor, each choosing between swerving or crashing. The difference however is that a tyrant has more power and influence than the poor. One aspect of game theory that we believe needs to be changed is that the size of the payoffs should matter.

As an example of something that plays no role in game theory, consider the concept of engagement. Multiplying the payoff matrix by the engagement does not change the max-min solution of game theory and is thus of no importance. Moreover, the payoff matrix strength is not relevant either. In physics, this is like saying that the charge of a particle does not influence its motion in a magnetic field, nor does the strength of the magnetic field. This is only true for a charge moving parallel to the field. The circulation around the field clearly depends on the charge as well as on the strength of the field.

The hard part is to disentangle the charge from the field strength. This is accomplished in physics by the field equations that say that charges and currents are the sources of the fields. Strong engagement leads to changes in the players behaviors through changes in their payoff and valuation fields. What is amazing however, is that engagement like viscosity enters the decision process theory equations in a non-linear way. Therefore, dramatically increasing or decreasing the engagement changes the qualitative behavior of the decision flow. You get an inkling of why when you realize that the engagement is itself a conserved flow and therefore contributes to the energy momentum of the system. It thus gets shared with other component parts.

Like viscosity, when the engagement is small it has almost no effect other than adjusting the time scale. As it gets larger, the non-linear nature of its behavior becomes evident. It is even possible that we might get “chaotic” or “turbulent” behaviors, though there is currently no basis for this conjecture. The following is the result of a computation (using a decision engineering notebook described in the Stationary Ownership Model Update white paper and implemented using a Mathematica notebook) in which the poor outnumber the tyrant by 10:1 and the engagement of the tyrant to the poor is 1:10.

We have the following interpretation of this picture. From a game theory perspective, the model has two Nash equilibriums. The poor see their strategy to be “swerve” and assume that the wealthy will “crash”. The wealthy see the opposite. This is one variant of the classic game of chicken. It is clear in the figure that by assuming the wealthy are much less engaged, we are closer to one of the Nash equilibrium: we see the Nash equilibrium of the poor, which is to “swerve” and for the wealthy to “crash”.

We see more however. Because of the inequality between the two players, the preference of the poor to crash is going to be smaller over time than for the wealthy to crash. So, in some sense, the wealthy crashing is not as devastating as it is for the poor. There is much less incentive for the wealthy to avoid the choice “swerve”.

The strategic flows add some interesting aspects to the story. The magnitude of the flows in this model run are all comparable. Nevertheless, they support the fact that the net behavior for the wealthy to swerve is zero and the net behavior of the wealthy to crash is small and positive. It is also clear that the net flow for the poor to swerve is much bigger than any of the other net flows.

We interpret this as follows. The poor will suffer and avoid the game of chicken. On average they will swerve. The wealthy will crash, making what appears to be the correct assumption that the poor will always swerve. These assumptions, however, rely on the small engagement of the wealthy. This appears to be the trademark of the tyrant They suffer no consequence for their action and are thus rewarded. The full decision process theory would go on to predict that the payoffs for the wealthy should not change since their source is small. The poor however might change their payoffs over time to better reflect what is happening.

Is there anything that can be done? One possibility is demand an equality of effort between the tyrant and the people, through laws, the courts or the press, as examples. An example computation is provided below, using a gravitational like field to force equality by imagining a potential well that is centered when the strategic effort of the poor matches the strategic effort of the tyrant.

The model generates a time component of the metric, which can be thought of as a “gravitational” field that pulls all strategies to this common center. We see the consequence of this in the above figure. We now expect that the tyrant will see consequences to their action, despite their initial lack of engagement. In fact it might be that that engagement will also change as a consequence.


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