Rich get Richer vs Wealth Tax

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Rupertpassphotoneu Rupert Nagler (Author)



Tagged by Rupert Nagler over 4 years ago


Tagged by Rupert Nagler over 4 years ago


Tagged by Rupert Nagler over 4 years ago


Tagged by Rupert Nagler over 4 years ago

wealth distribution 

Tagged by Rupert Nagler over 4 years ago

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Rich get Richer vs Wealth Tax.nlogo

Author: Rupert Nagler, Jan 2020,


"The rich get richer" - you can hear it everywhere today. But why? Playing with this model you will learn and understand the intrinsic workings of multiplicative growth and a possible remedy. We abstract economic transactions by simulating a bilateral coin game played pairwise by a set of turtles sitting on a blue 2d-world. The vertical position reflects their actual wealth, the horizontal position the turtle's unique who number. Currently playing pairs are pictured by a link. Lorenz Curve, Gini Coefficient and a histogram show the actual distribution of wealth. You can explore the effects of cumulative growth obscured by the misleading ergodic hypothesis in traditional economics and the benefits of cooperation induced by a form of wealth-tax. Idea influenced by Ole Peters, LML, see:


  • A fraction "select-ratio" of turtles throw a coin pairwise at each tick, the bet is a fraction "transfer-ratio" of the minimum of the wealth of both turtles.
  • For the looser the bet is multiplied by "loose-mult" and then subtracted from his wealth. For the winner the bet is multiplied by "win-mult" and then added to his wealth.
  • After all pairs have thrown their coins and their wealth was transferred, some redistribution in the form of a wealth-tax may be applied: If "tax-factor" is > 0 and wealth is > "tax-limit" a wealth tax (wealth * tax-factor) is subtracted. Then the collected wealth tax is redistributed evenly to all turtles or to the poor turtles below tax-limit, depending on the switch "redist-all?".
  • So you can simulate the effects of cooperation thru risk-sharing between players.


  • Use the sliders to control the number of turtles "num-turtles" and the initial wealth "init-wealth".
  • If you switch "random-init-wealth?" to "off" each turtle receives the equal "init-wealth" wealth. If you switch "random-init-wealth?" to "on" each turtle receives a random wealth between 1 and "init-wealth".
  • Set the fraction of the minimum wealth of both turtles "leverage" to bet and the fraction of all turtles to play in one tick "selection-ratio".
  • Set the multiplicative factors "loose-mult", "win-mult" (default: 1.0) to be applied to the transfer of the bet.
  • Optional set a "tax-factor", "tax-limit", and "redist-all?"
  • If you want bancrupt turtles to die, set "turtles-die?" to on.
  • To initialize the simulation "setup".
  • To play one round press "go-1", to play as long as you wish, press "go".


  • You see all turtles sitting on the black world area. Each turtle will go up or down vertically dependent of its current wealth after each tick.
  • Each pair of turtles (link) engaged in throwing a coin is connected by a line.
  • In the wealth-plot you see min, max, mean and median of the turtles wealth on a log10 scale.
  • In the wealth-distribution histogramm you see the number of turtles in different classes of wealth.
  • In the Lorenz Plot you see the actual shape of the Lorenz Curve.
  • In the Gini Plot you see the value of the Gini Coefficient over time.


  • Try different values for multiplicative growth ("loose-mult", "win-mult"),
  • Compare the wealth-distribution for no multiplicative growth (set both "loose-mult", "win-mult" to 1.0) to other values of multiplicative growth (eg. 0.6, 1.5)
  • Try different "tax-factor"s and "tax-limits", switch "redist-all?" on/off.
  • What effects can you see in the histogram, Gini Plot and Lorenz Curve?


  • better visualization ideas?
  • turtles get children and die of age
  • implement inheritance tax


  • using turtle world to show turtle ranking by position,
  • histogram on varying upper and lower bounds,



credit: computation of lorenz curve and gini index copied from: NetLogo models WealthDistribution

in-depth readings:

Wikipedia: Distribution of wealth, retrieved 12/2019

Wikipedia: Lorenz Curve, retrieved 12/2019

Wikipedia: Gini Coefficient, retrieved 12/2019

Wikipedia: Ergodic process, retrieved 12/2019

Ergodicity Economics, Ole Peters and Alexander Adamou, 2018

Entrepreneurs, Chance, and the Deterministic Concentration of Wealth, Joseph E. Fargione u.a., 2011

An evolutionary advantage of cooperation, Ole Peters and Alexander Adamou, 2018

Capital and Ideology, Thomas Piketty, 2019

Farmers Fable: Simulation benefits of cooperation, retrieved 12/2019

Gier, Marc Elsberg, novel, blanvalet 2019


Copyright 2020 Rupert Nagler, All rights reserved. Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed:

  • this copyright notice is included.
  • this model will not be redistributed for profit without permission from Rupert Nagler.

Contact the author for appropriate licenses for redistribution for profit.

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; Rich get Richer vs Wealth Tax.nlogo; Rupert Nagler Jan 2020

  gini-index-reserve ; actual gini %
  lorenz-points ; list of lorenz-points
  count-notax-turtles ; number of turtles paying no tax
  ; win-mult and loose-mult are global growthrates to introduce multiplicative growth
  ; for positive growth set loose-mult < win-mult
  ; additrive growth is interinsic as bet is moved from looser to winner

turtles-own [
  wealth ; actual wealth of turtle
  tax ; actual amount of wealth tax turtle has payed

to setup
  ask patches [set pcolor 73]
  set count-notax-turtles 0

to setup-turtles
  create-turtles num-turtles [
    set heading 0
    set color yellow
    set shape "circle"
    ifelse random-init-wealth? [ ; random distributuion
      set wealth random-float init-wealth
    ][ ; equal distribution
      set wealth init-wealth
    set tax 0
    ; place turtle on plain according id(own) on x-axsis and wealth on y-axsis
    setxy (who / num-turtles * 100) wealth

to go
  clear-links ; delete all links of player pairs from old round
  if count turtles < 2 [stop]

to gaming ; build random list of all turtles participating in new game round
  let game-turtles [self] of n-of (count turtles * select-ratio) turtles
  while [length game-turtles > 1] [ ; select a pair and transfer bet
    let tlooser one-of game-turtles ; select looser and remove from list
    set game-turtles remove tlooser game-turtles
    let twinner one-of game-turtles ; select winner and remove from list
    set game-turtles remove twinner game-turtles
    let minwealth min list [wealth] of tlooser [wealth] of twinner ; compute lower wealth
    let diffwealth (minwealth * leverage) ; amount to bet
    ask twinner [ ; winner receives bet, multiplicated by winners growth rate
      set wealth wealth + (diffwealth * win-mult)
    ask tlooser [; looser pays bet, multiplicated by loosers growth rate
      set wealth wealth - (diffwealth * loose-mult)
      create-link-to twinner

to taxing
  if tax-factor > 0 [ ; do we have to compute taxes?
    let notax-turtles [self] of no-turtles ; empty unsorted list of turtles
    let sumtax 0
    ask turtles [ ; pay wealth tax
      ifelse wealth > tax-limit [ ; is there a tax to pay?
          set tax wealth * tax-factor
          set wealth wealth - tax ; turtle pays tax
          set sumtax sumtax + tax ; add to total tax collected
        ] [
          set tax 0
          set notax-turtles lput self notax-turtles ; add to list of notax-turtles
    set count-notax-turtles length notax-turtles ; number of notax-turtles
    ifelse (redist-all?) or (count-notax-turtles <= 0) [ ; do we have to redistribute to all turtles?
      let mtax (sumtax / count turtles) ; divide total tax between all turtles
      ask turtles [ ; distribute tax collected to all turtles
        set wealth wealth + mtax ; redistribute
    ] [ ; distribute tax collected only to no-tax-turtles
        let mtax (sumtax / count-notax-turtles) ; divide total tax between all no-tax-turtles
        ask turtle-set notax-turtles [ ; changes list into agentset
          set wealth wealth + mtax ; redistribute

to moving
  ask turtles [
    if turtles-die? [ ; should bancrupt turtles die?
      if wealth < 1.0E-10 [die]
    ] ; move turtles to their y-position according to their wealth
    set ycor (wealth + min [wealth] of turtles) / max [wealth] of turtles * 100

to update-lorenz-and-gini
  ; recompute value of gini-index-reserve and the points in lorenz-points for the Lorenz and Gini-Index plots
  let sorted-wealths sort [wealth] of turtles
  let total-wealth sum sorted-wealths
  let wealth-sum-so-far 0
  let index 0
  let c-turtles count turtles
  set gini-index-reserve 0
  set lorenz-points []
  ; now actually plot the Lorenz curve -- along the way, we also calculate the Gini index
  repeat c-turtles [
    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 / c-turtles) - (wealth-sum-so-far / total-wealth)

There is only one version of this model, created over 4 years ago by Rupert Nagler.

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