In CmLab we explore the implications of the phenomenon of Conservation of Money in a modern economy. This is one of a series of models exploring the dynamics of sustainable economics – PSoup, ModEco, EiLab, OamLab, MppLab, TpLab, CmLab.

There is a new type of economic model called a capital exchange model, in which the biophysical economy is abstracted away, and the interaction of units of money is studied. Benatti, Drăgulescu and Yakovenko described at least eight capital exchange models – now referred to collectively as the BDY models – which are replicated as models A through H in EiLab. In recent writings, Yakovenko goes on to show that the entropy of these monetarily isolated systems rises to a maximal possible value as the model approaches steady state, and remains there, in analogy of the 2nd law of thermodynamics. EiLab demonstrates this behaviour. However, it must be noted that we are NOT talking about thermodynamic entropy. Heat is not being modeled – only simple exchanges of cash. But the same statistical formulae apply.

In three unpublished papers and a collection of diary notes and conference presentations (all available with this model), the concept of “entropic index” is defined for use in agent-based models (ABMs), with a particular interest in sustainable economics. Models I and J of EiLab are variations of the BDY model especially designed to study the Maximum Entropy Principle (MEP – model I) and the Maximum Entropy Production Principle (MEPP – model J) in ABMs. Both the MEPP and H.T. Odum’s Maximum Power Principle (MPP) have been proposed as organizing principles for complex adaptive systems. The MEPP and the MPP are two sides of the same coin, and an understanding of their implications is key, I believe, to understanding economic sustainability. Both of these proposed (and not widely accepted) principles describe the role of entropy in non-isolated systems in which complexity is generated and flourishes, such as ecosystems, and economies.

EiLab is one of several models exploring the dynamics of sustainable economics – PSoup, ModEco, EiLab, OamLab, MppLab, TpLab, and CmLab.

In 1985 Dr Michael Palmiter, a high school teacher, first built a very innovative agent-based model called “Simulated Evolution” which he used for teaching the dynamics of evolution. In his model, students can see the visual effects of evolution as it proceeds right in front of their eyes. Using his schema, small linear changes in the agent’s genotype have an exponential effect on the agent’s phenotype. Natural selection therefore happens quickly and effectively. I have used his approach to managing the evolution of competing agents in a variety of models that I have used to study the fundamental dynamics of sustainable economic systems. For example, here is a brief list of some of my models that use “Palmiter Genes”:
- ModEco - Palmiter genes are used to encode negotiation strategies for setting prices;
- PSoup - Palmiter genes are used to control both motion and metabolic evolution;
- TpLab - Palmiter genes are used to study the evolution of belief systems;
- EffLab - Palmiter genes are used to study Jevon’s Paradox, EROI and other things.

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EiLab - Model I - is a capital exchange model. That is a type of economic model used to study the dynamics of modern money which, strangely, is very similar to the dynamics of energetic systems. It is a variation on the BDY models first described in the paper by Dragulescu and Yakovenko, published in 2000, entitled “Statistical Mechanics of Money”. This model demonstrates the ability of capital exchange models to produce a distribution of wealth that does not have a preponderance of poor agents and a small number of exceedingly wealthy agents.

This is a re-implementation of a model first built in the C++ application called Entropic Index Laboratory, or EiLab. The first eight models in that application were labeled A through H, and are the BDY models. The BDY models all have a single constraint - a limit on how poor agents can be. That is to say that the wealth distribution is bounded on the left. This ninth model is a variation on the BDY models that has an added constraint that limits how wealthy an agent can be? It is bounded on both the left and right.

EiLab demonstrates the inevitable role of entropy in such capital exchange models, and can be used to examine the connections between changing entropy and changes in wealth distributions at a very minute level.

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EffLab was built to support the study of the efficiency of agents in an evolving complex adaptive system. In particular:
- There is a definition of efficiency used in ecology, and an analogous definition widely used in business. In ecological studies it is called EROEI (energy returned on energy invested), or, more briefly, EROI (pronounced E-Roy). In business it is called ROI (dollars returned on dollars invested).
- In addition, there is the more well-known definition of efficiency first described by Sadi Carnot, and widely used by engineers. It is usually represented by the Greek letter ‘h’ (pronounced as ETA). These two measures of efficiency bear a peculiar relationship to each other: EROI = 1 / ( 1 - ETA )

In EffLab, blind seekers wander through a forest looking for energy-rich food. In this multi-generational world, they live and reproduce, or die, depending on whether they can find food more effectively than their contemporaries. Data is collected to measure their efficiency as they evolve more effective search patterns.

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This model describes and analyses the outcomes of the confrontation of interests, some conflicting, some common, about the management of a small river in SW France

First Version

The objective of the model is to evaluate the impact of seasonal forecasts on a farmer’s net agricultural income when their crop choices have different and variable costs and returns.

This model simulates the dynamics of eighteenth-century infantry battle tactics. The goal is to explore the effect of different tactics and individual traits in the dynamics of the combat.

Package for simulating the behavior of experts in a scientific-forecasting competition, where the outcome of experiments itself depends on expert consensus. We pay special attention to the interplay between expert bias and trust in the reward algorithm. The package allows the user to reproduce results presented in arXiv:2305.04814, as well as testing of other different scenarios.