Thank you, Marco, for your comments and your questions. There are many aspects to your questions that I have had to think about. Let me try to address them one at a time.

**About variations:** There are several variations of the so-called BDY (Benatti-Drăgulescu-Yakovenko) capital exchange models. Drăgulescu and Yakovenko (2000) described seven of the eight models that they studied. The eighth model was said to be too detailed to describe in that paper, because it involved banking. They claimed all eight models lead to a distribution of wealth that mimicked either an exponential distribution of energy, or a Maxwell-Boltzmann-like distribution of energy. The only deciding factor was whether the exchange was symmetric in time, or asymmetric in time. For example, if A paid B $C, and then they immediately had to switch roles, did B pay back the same amount, reinstating the previous state? If the answer was “yes”, then the exponential distribution appeared. It mattered not if the amount exchanged was $1 or 10$. If the answer was “no” then the Maxwell-Boltzmann distribution appeared. An example of an exchange that is asymmetric in time is a transfer of a percentage of one’s wealth. One of their described models even used a very complex stochastic implementation of a Cobb-Douglas production function to determine who employs, who gets hired, at what wage, what widgets are built, who buys the widgets, and for how much. The model that they did not describe involved banks. EiLab contains my implementation of the seven BDY models they described. CmLab is my own version of a banking model. I can confirm their observations about time symmetry. Only two types of distribution appear as the ultimate high-entropy distributions of wealth.

**Justification of Application to Economic Data** – Do these BDY models demonstrate the same mechanisms as is found in real economies? These types of models are sometimes called “kinetic wealth exchange models” (KWEMs). The exchange of kinetic energy in models of ideal gases is a binary event in which a conserved quantity (energy) is exchanged. That is a very thoroughly-studied phenomenon in physics, going back to the days of Maxwell, Boltzmann and Gibbs in the late 1800s. The exchange of modern money in any economy is also a binary event in which a conserved quantity (money) is exchanged. The key elements of the exchange are identical, whether we are dealing with kinetic energy or money. The question is, what do we mean by “identical”?

• All transactions are binary, involving only two agents;

• The exchanged quantity is conserved in the binary transaction (i.e. can be described by a continuity equation);

• The determination of which two agents interact is stochastic.

In the various models tested by D&Y, and those tested by me, the amount exchanged, the nature of the exchange, the constraints on the exchange (e.g. whether an agent is bankrupt), or the other conditions of the agents selected for the exchange (e.g. levels of wealth, or roles as employer or employee) – none of these have any significant effect on the ultimate distribution of wealth, other than the time-symmetry or time-asymmetry of the exchange mechanism. The distribution of wealth always asymptotically approaches one in which entropy is maximized, for that distribution.

**Are Skilled Agents Differentially Enfranchised:** In the KWEMs, does a wealthy person have more access to the economy? Yes, they do, except in my “Model I”. But, this does not change the ultimate equilibrium distribution. In the real world, does an educated, skilled, or intelligent person have more access to the economy? Yes, but this does not change the ultimate equilibrium distribution by much. It has a small effect on the ultimate shape of the empirically-determined equilibrium distribution, often called a “fat tail”. There is a lot of literature discussing the “fat tails” of the empirically measured wealth distributions in which there are slightly more wealthy people than predicted by KWEMs. However, there are many who argue that this effect is minor, compared to the dominant role of the effects of maximizing entropy. Those personal attributes of individuals (education, skill, wealth, determination) might decide who rises to the top, but they do not have much effect on the ultimate shape of the distribution.

Does Network Connectivity Matter: In physics, ideal gas atoms only interact with those in a small immediate neighbourhood, determined by their ever-changing intersecting trajectories, and their speeds, and by the mean path distance between collisions. I suspect that such a constraint would be describable as a “small world network”, but I am uncertain. In the BDY models, the pairing of agents for any given exchange is not limited in this way. Any agent can interact with any agent. To be honest, I don’t know what such a network would be called, so I’ll refer to it as a “universal network”. In my model called ModEco, agents can only interact with agents in a small neighbourhood. In that case, I have implemented a kind of small world network, and the ultimate wealth distribution is a Maxwell-Boltzmann-like distribution. It would be interesting to add a “small world network” contact constraint within a BDY model to see if it has any affect on the ultimate shape of the equilibrium distribution. Based on my experience so far, I expect that it would not.

**Exploitation of Symmetries (of Universals):** One of the philosophical foundations of science is symmetry of application. There are universal dynamics that appear in many kinds of stochastic systems - systems that are otherwise apparently not associated. A carefully constructed ABM can demonstrate (not simulate) these universals. The “stylized statistics” that can be gathered from such universal dynamics as seen in ABMs can teach us how to understand all of those other dynamic systems that share the same universal dynamic behaviours – that share the same “stylized statistics”. This is a fundamental philosophical argument.

The exploitation of such symmetries is a means to transfer knowledge from one discipline to another – with care. The causes and effects of rising entropy in ABMs is one such universal – one such symmetry – that can shed a lot of light on the murky dynamics of ecosystems, of social systems and of economic systems.

The fact that “Model I” has shown clear evidence of sharing a universal with statistical chemistry, with statistical mechanics, and with empirical economic data, implies to me that there are bridges to be built and exploited using ABMs.