Sugarscape 3 Wealth Distribution

Sugarscape 3 Wealth Distribution preview image

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Uri_dolphin3 Uri Wilensky (Author)


social science 

Tagged by Reuven M. Lerner about 5 years ago

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This third model in the NetLogo Sugarscape suite implements Epstein & Axtell's Sugarscape Wealth Distribution model, as described in chapter 2 of their book Growing Artificial Societies: Social Science from the Bottom Up. It provides a ground-up simulation of inequality in wealth. Only a minority of the population have above average wealth, while most agents have wealth near the same level as the initial endowment.

The inequity of the resulting distribution can be described graphically by the Lorenz curve and quantitatively by the Gini coefficient.


Each patch contains some sugar, the maximum amount of which is predetermined. At each tick, each patch regains one unit of sugar, until it reaches the maximum amount.
The amount of sugar a patch currently contains is indicated by its color; the darker the yellow, the more sugar.

At setup, agents are placed at random within the world. Each agent can only see a certain distance horizontally and vertically. At each tick, each agent will move to the nearest unoccupied location within their vision range with the most sugar, and collect all the sugar there. If its current location has as much or more sugar than any unoccupied location it can see, it will stay put.

Agents also use (and thus lose) a certain amount of sugar each tick, based on their metabolism rates. If an agent runs out of sugar, it dies.

Each agent also has a maximum age, which is assigned randomly from the range 60 to 100 ticks. When the agent reaches an age beyond its maximum age, it dies.

Whenever an agent dies (either from starvation or old age), a new randomly initialized agent is created somewhere in the world; hence, in this model the global population count stays constant.


The INITIAL-POPULATION slider sets how many agents are in the world.

The MINIMUM-SUGAR-ENDOWMENT and MAXIMUM-SUGAR-ENDOWMENT sliders set the initial amount of sugar ("wealth") each agent has when it hatches. The actual value is randomly chosen from the given range.

Press SETUP to populate the world with agents and import the sugar map data. 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-VISION is selected the agents with the longest vision will be darkest and, similarly, when COLOR-AGENTS-BY-METABOLISM is selected the agents with the lowest metabolism will be darkest.

The WEALTH-DISTRIBUTION histogram on the right shows the distribution of wealth.

The LORENZ CURVE plot shows what percent of the wealth is held by what percent of the population, and the the GINI-INDEX V. TIME plot shows a measure of the inequity of the distribution over time. A GINI-INDEX of 0 equates to everyone having the exact same amount of wealth (collected sugar), and a GINI-INDEX of 1 equates to the most skewed wealth distribution possible, where a single person has all the sugar, and no one else has any.


After running the model for a while, the wealth distribution histogram shows that there are many more agents with low wealth than agents with high wealth.

Some agents will have less than the minimum initial wealth (MINIMUM-SUGAR-ENDOWMENT), if the minimum initial wealth was greater than 0.


How does the initial population affect the wealth distribution? How long does it take for the skewed distribution to emerge?

How is the wealth distribution affected when you change the initial endowments of wealth?


All of the Sugarscape models create the world by using file-read to import data from an external file, sugar-map.txt. This file defines both the initial and the maximum sugar value for each patch in the world.

Since agents cannot see diagonally we cannot use in-radius to find the patches in the agents' vision. Instead, we use at-points.


Other models in the NetLogo Sugarscape suite include:

  • Sugarscape 1 Immediate Growback
  • Sugarscape 2 Constant Growback

For more explanation of the Lorenz curve and the Gini index, see the Info tab of the Wealth Distribution model. (That model is also based on Epstein and Axtell's Sugarscape model, but more loosely.)


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


If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:


Copyright 2009 Uri Wilensky.


This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at

Comments and Questions

Missing File in Sugarscape 3 Model? (Question)

I think there must be a setup file missing called 'sugar-map.txt' from the download of the SugarScape 3 Wealth Distribution model. I deleted the file-open command and set psugar to maximum-sugar-endowment (in the setup procedure) and it seemed to work fine. I suspect that the wealth distribution curve is a gamma curve rather than a Pareto curve. Just guessing! Garvin H Boyle

Posted over 3 years ago

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globals [

turtles-own [
  sugar           ;; the amount of sugar this turtle has
  metabolism      ;; the amount of sugar that each turtles loses each tick
  vision          ;; the distance that this turtle can see in the horizontal and vertical directions
  vision-points   ;; the points that this turtle can see in relative to it's current position (based on vision)
  age             ;; the current age of this turtle (in ticks)
  max-age         ;; the age at which this turtle will die of natural causes

patches-own [
  psugar           ;; the amount of sugar on this patch
  max-psugar       ;; the maximum amount of sugar that can be on this patch

;; Setup Procedures

to setup
  if maximum-sugar-endowment <= minimum-sugar-endowment [
    user-message "Oops: the maximum-sugar-endowment must be larger than the minimum-sugar-endowment"
  create-turtles initial-population [ turtle-setup ]

to turtle-setup ;; turtle procedure
  set color red
  set shape "circle"
  move-to one-of patches with [not any? other turtles-here]
  set sugar random-in-range minimum-sugar-endowment maximum-sugar-endowment
  set metabolism random-in-range 1 4
  set max-age random-in-range 60 100
  set age 0
  set vision random-in-range 1 6
  ;; turtles can look horizontally and vertically up to vision patches
  ;; but cannot look diagonally at all
  set vision-points []
  foreach n-values vision [? + 1]
    set vision-points sentence vision-points (list (list 0 ?) (list ? 0) (list 0 (- ?)) (list (- ?) 0))
  run visualization

to setup-patches
  file-open "sugar-map.txt"
  foreach sort patches
    ask ?
      set max-psugar file-read
      set psugar max-psugar

;; Runtime Procedures

to go
  if not any? turtles [
  ask patches [
  ask turtles [
    set age (age + 1)
    if sugar <= 0 or age > max-age [
      hatch 1 [ turtle-setup ]
    run visualization

to turtle-move ;; turtle procedure
  ;; consider moving to unoccupied patches in our vision, as well as staying at the current patch
  let move-candidates (patch-set patch-here (patches at-points vision-points) with [not any? turtles-here])
  let possible-winners move-candidates with-max [psugar]
  if any? possible-winners [
    ;; if there are any such patches move to one of the patches that is closest
    move-to min-one-of possible-winners [distance myself]

to turtle-eat ;; turtle procedure
  ;; metabolize some sugar, and eat all the sugar on the current patch
  set sugar (sugar - metabolism + psugar)
  set psugar 0

to patch-recolor ;; patch procedure
  ;; color patches based on the amount of sugar they have
  set pcolor (yellow + 4.9 - psugar)

to patch-growback ;; patch procedure
  ;; gradually grow back all of the sugar for the patch
  set psugar min (list max-psugar (psugar + 1))

to update-lorenz-and-gini
  let num-people count turtles
  let sorted-wealths sort [sugar] of turtles
  let total-wealth sum sorted-wealths
  let wealth-sum-so-far 0
  let index 0
  set gini-index-reserve 0
  set lorenz-points []
  repeat num-people [
    set wealth-sum-so-far (wealth-sum-so-far + item index sorted-wealths)
    set lorenz-points lput ((wealth-sum-so-far / total-wealth) * 100) lorenz-points
    set index (index + 1)
    set gini-index-reserve
      gini-index-reserve +
      (index / num-people) -
      (wealth-sum-so-far / total-wealth)

;; Utilities

to-report random-in-range [low high]
  report low + random (high - low + 1)

;; Visualization Procedures

to no-visualization ;; turtle procedure
  set color red

to color-agents-by-vision ;; turtle procedure
  set color red - (vision - 3.5)

to color-agents-by-metabolism ;; turtle procedure
  set color red + (metabolism - 2.5)

; Copyright 2009 Uri Wilensky.
; See Info tab for full copyright and license.

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