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by Klaus G. Troitzsch (Submitted: 06/19/2013)

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## ## WHAT IS IT?

Much like Epstein & Axtell's Sugarscape, this virtual world is populated with agents which move around on a grid on whose patches food grows and grows back constantly, and over-harvested patches can regrow when seed floats in frm neighbouring patches. Agents harvest and either eat or add the harvested food to their "wealth". Agents have a limited lifetime, and they can die from starving. Besides they reproduce. All of these actions satisfy their needs of survival, wealth, reproduction and information. Moreover they have a need of being influential which is an incentive to co-ordinate other agents. Co-ordination means that co-ordinating agents collect information from their (volunteer) subordinates and forward this information back to all their current subordinates which gives both co-ordinators and subordinates a wider range of vision such that their chance to move to more promising patches increases. The decision to co-ordinate, subordinate, end co-ordinating or end subordinating and all other decisions (to eat, to harvest, to move, to reproduce) depend on the expected utility of the respective action which in turn is calculated as a weighted sum of degrees of satisfaction of the needs mentioned above. The decision is probabilistic, such that the action with the least utility is never taken whereas the other actions are taken with a probability proportional to the expected utility.


Each patch contains some food, the maximum amount of which is predetermined. At each tick, the food on each patch grows at a fixed rate, until it reaches the maximum amount. The amount of food a patch currently contains is indicated by its color; the darker the green, the more food.

At setup, agents are placed at random within the world. Each agent can only see a certain square neighbourhood around itself which it copies into its memory. When moving, the memory is updated, and older information is forgotten after some time, apart from the fact that it becomes obsolete when other agents harvest or move around in the part of the world which is still remembered but not visible any longer. At each tick, each agent can decide to move to the nearest unoccupied location within their vision range with the most food, and collect all or part of the food there, or it decides to take one of the other possible actions, depending their respective utilities.

Agents also eat as much food as they need in each tick, based on their metabolism rates. If an agent runs out of food, it dies.

If an agents has decided to subordinate to an agent which has signalised that it feels fit to co-ordinate other agents, it reports its memory to the co-ordinator, receives the content of the memory of the latter and gives part of its wealth to the co-ordinator.


Set the INITIAL-POPULATION slider before pressing SETUP. This determines the number of agents in the world.

Press SETUP to populate the world with agents. GO will run the simulation continuously, while GO ONCE will run one tick.

The VISUALIZATION chooser gives different visualization options and may be changed while the GO button is pressed. When NO-VISUALIZATION is selected all the agents will be red. When COLOR-AGENTS-BY-METABOLISM is selected the agents with the lowest metabolism will be darkest.

The four plots show the world population over time including the numbers of agents who are currently co-ordinators, subordinates and autonomous, the average food per agent, the average duration of subordination relations and the phase diagram of amount of food and number of agents.


Usually there is no stable population size and no stable worldwide food amount. Rather these two output parameters oscillate with an decreasing amplitude in a generalised Lotka-Volterra manner. Under certain input parameter combinations agents will die out when the carrying capacity is exceeded or when the remaining food cannot be reached early enough by the remaining agents.


To which extent does the sustainability of the model depend on the feature that agents can co-ordinate and subordinate, respectively? Switch "enable hierarchy" off and see what happens.




This model uses a small part of the code of:
- Li, J. and Wilensky, U. (2009). NetLogo Sugarscape 2 Constant Growback model. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

and the NetLogo software:
- Wilensky, U. (1999). NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.


Epstein, J. and Axtell, R. (1996). Growing Artificial Societies: Social Science from the Bottom Up. Washington, D.C.: Brookings Institution Press.

The original (JAVA) version of this model was first published in:

König, A., Möhring, M., & Troitzsch, K. G. (2003). Agents, Hierarchies and Sustainability. In F. Billari, & A. Prskawetz, Agent-Based Computational Demography (S. 197–210). Heidelberg: Physica.

The NetLogo replication was first written by Florian Zink in his master thesis and finished by Klaus G. Troitzsch for his paper in Leitner, Stephan; Wall, Friederike (Eds.): Artificial Economics and Self Organization. Agent-Based Approaches to Economics and Social Systems. Series: Lecture Notes in Economics and Mathematical Systems, Vol. 669, Heidelberg: Springer 2013 (to appear on August 31, 2013,


Klaus G. Troitzsch 2013:


(c) 2013 Klaus G. Troitzsch

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