Ndtyjky

The problem I’m dealing with at the moment involves a system described in the Guanzi. A large section of the book is about how governments should work to extract a surplus from the economy which they can redistribute to ensure the loyalty of existing followers and gain new ones. Under this system, whoever can redistribute the most wealth becomes the overall leader. However, he also has to out-compete the other individuals in the system: they are all busy trying to establish their own redistribution networks.

The result is a series of pyramid-shaped redistribution networks, both independent and nested.

Simplified visual representation of the expected outcome

These are dynamic across time and space. Gaining resources lets you acquire more followers, which in turn gives you access to more resources. There is also a random component involved: a bad harvest or a war may wipe out your resources. If one leader runs out of resources (whether as a result of a disaster or because he redistributed them too generously among his followers), he will either be supplanted by a follower or his network will collapse and its members leave to join other networks.

I think it is possible to model this algorithmically.

We can assume that willingness to share resources is innate.

Generosity = propensity score

An individual acquires followers as a function of both the surplus resources he possesses and his willingness to share them.

Followers[tn] = Surplus[t-1] * Generosity

It is worth noting that growth is endogenous in this model. It is a product of whatever economic growth coefficient is deemed realistic given technology and natural resources (a), as well as of the previous cycle’s surplus and the number of followers an individual has, on the basis that these constitute factors of production. (Note: I'm not interested in getting actual monetary values out of this, just modelling the relationships. I understand that if you plugged real numbers into it people would end up redistributing more than they own.)

Growth = a (Surplus[t-1] * Followers[t-1])

At T=0 the surplus enjoyed by each individual in the system must be generated randomly.

Surplus[t0] = randomly generated number

Followers generate additional resources for their leader, but they also need to be remunerated, meaning that they simultaneously deplete their leader’s resources, proportional to his generosity propensity score. A random component must also be included, as mentioned above, to account for famines, bumper crops, wars etc.

Surplus[tn] = Random Component (Surplus[t-1] + Growth) – (Followers[t-1] * Generosity)

Once these relationships have been defined, then the algorithm is relatively simple:

T1:
Each individual checks the Surplus*Generosity score of the nearest individual who is not already following him. If Individual A’s SG > Individual B’s SG, then Individual B moves closer to Individual A and becomes his follower. (Note: If individual B has followers of his own, he carries them with him. Also: Followers automatically re-check their leader's SG in every round, since he is the closest individual to them. They will leave his network to become free agents once more if his SG drops below their own.)

Otherwise, he does nothing.

T2 :
Each individual’s stats (Followers, Surplus) are recalculated based on the new situation.
Step 1 is repeated.

T3 :
Repeat previous step

One would expect the individuals with the optimal generosity score to build the biggest networks, as they acquire followers without completely depleting their resources.

I suspect – but am not sure – that this model’s characteristics are similar to those of an L-system model.

• Individuals are programmed with a simple instruction: “If the person closest to you has a higher S*G score than you do, approach and follow him.”


• On the basis of this the individuals form structures (from the perspective of the individual with the optimal S*G score, they appear to cluster around him in a semi-structured way)


• These structures grow with every successive time period


• They collapse after depleting their own resources, or when a random disaster strikes.


• After a collapse, the process automatically begins again.

However, I'm not a maths or a computing guy (I'm a Chinese philosophy guy) so I'm not sure if I'm just being fooled by a superficial resemblance or not. Is this a genuine example of string rewriting or am I just convincing myself it is because you get tree-like structures out of it? Is this even a model that can work at all? Have I totally messed up my equations? (I haven't done this since high school, so it's highly probable.)

All help is gratefully received.