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# Throwing Coins  Inequality and Tax.nlogo
Author: Rupert Nagler, Jan 2020, nagler@idi.co.at
## WHAT IS IT?
Simulation of a coin game based on multiplicative growth. Based on the paper "**Ergodicity Economics**", published 2018 by Ole Peters and Alexander Adamou @ London Mathematical Laboratory: _"We toss a coin, and if it comes up heads we increase your monetary wealth by 50%; if it comes up tails we reduce your wealth by 40%. We’re not only doing this once, we will do it many times. Would you submit your wealth to the dynamic our game will impose on it?"_, see: https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf
Our turtles assume they will get rich playing this game. They are presented in their blue 2dworld as yellow circles. Their vertical position reflects their actual wealth, the horizontal position is their unique "who" number. You will experience their fate mislead by a **wrong ergodic hypothesis** for multiplicative growth  like most traditional economists. You can explore the intrinsic effects why **"the rich get richer"** and the benefits of **cooperation** induced by a form of wealthtax. Lorenz Curve, Gini Coefficient and a histogram show the current distribution of their wealth.
## HOW IT WORKS
All turtles play the coin game. Each of them throws a coin at each tick: If heads are shown, individual wealth is multiplied by "multheads" and "addheads" is added. If tails are shown, individual wealth is multiplied by "multtails" and "addtails" is added. After all turtles have thrown their coins and their wealth was adopted, some redistribution in the form of a wealthtax may be applied: If "taxfactor" is > 0 and wealth is > "taxlimit" a wealth tax (wealth * taxfactor) is subtracted. Then the collected wealth tax is redistributed evenly to all turtles or to the poor turtles below taxlimit, depending on the switch "redistall?". So you can simulate the effects of cooperation sharing the risk between players.
## HOW TO USE IT
* Use the sliders to control the number of turtles "numturtles" and the initial wealth "initwealth". * If you switch "randominitwealth?" to "off" each turtle receives the equal "initwealth" wealth; if you switch "randominitwealth?" to "on" each turtle receives a random wealth between 1 and "initwealth". * Set the fraction of actual wealth to bet by "leverage" (default: 1.0). * Set the multiplicative factors "multheads", "multtails" (defaults: 0.6, 1.5) with which your bet will be multiplied in case of win / loss. * Set the additive values "addheads", "addtails" (defaults: 0.0, 0.0) which will be added to your bet in case of win / loss. * Optional set "taxfactor", "taxlimit", and "redistall?" * If you want bancrupt turtles to die, set "turtlesdie?" to on. * To setup the simulation, press "setup". * To play one round press "go1", to play as long as you wish, press "go".
## THINGS TO NOTICE
* You see all turtles sitting on the blue world area. Each turtle will go up or down vertically dependent of its current wealth after each tick. * In the wealthplot you see min, max, mean and median of the turtles wealth on a log10 scale. * In the wealthdistribution 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.
## THINGS TO TRY
* Try different values for multiplicative growth ("headsmult", "tailsmult") and additive growth ("addheads", "addtails"), * Compare the wealthdistribution for no multiplicative growth (set both "headsmult", "tailsmult" to 1.0) to other values of multiplicative growth (eg. 0.6, 1.5) * Compare the wealthdistribution for no additive growth (set both "headsadd", "tailsadd" to 0.0) to other values of additive growth (eg. 0.2, 0.3) * Try different "taxfactor"s and "taxlimit"s, switch "redistall?" on/off. * What changes can you see in the histogram, Gini Plot and Lorenz Curve?
## EXTENDING THE MODEL
* better visualization ideas? * turtles get children and die of age * implement inheritance tax
## NETLOGO FEATURES
* plotting on a log scale, * using turtle world to show turtle ranking by position, * histogram on varying upper and lower bounds,
## RELATED MODELS
http://ccl.northwestern.edu/netlogo/models/WealthDistribution http://ccl.northwestern.edu/netlogo/models/Sugarscape3WealthDistribution
## CREDITS & REFERENCES
credit: computation of lorenz curve and gini index copied from: NetLogo models WealthDistribution
indepth readings:
Wikipedia: Distribution of wealth, retrieved 12/2019 https://en.wikipedia.org/wiki/Distribution_of_wealth
Wikipedia: Lorenz Curve, retrieved 12/2019 https://en.wikipedia.org/wiki/Lorenz_curve
Wikipedia: Gini Coefficient, retrieved 12/2019 https://en.wikipedia.org/wiki/Gini_coefficient
Wikipedia: Ergodic process, retrieved 12/2019 https://en.wikipedia.org/wiki/Ergodic_process
Ergodicity Economics, Ole Peters and Alexander Adamou, 2018 https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf
Entrepreneurs, Chance, and the Deterministic Concentration of Wealth, Joseph E. Fargione u.a., 2011 https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0020728&type=printable
An evolutionary advantage of cooperation, Ole Peters and Alexander Adamou, 2018 https://arxiv.org/pdf/1506.03414.pdf
Capital and Ideology, Thomas Piketty, 2019 http://piketty.pse.ens.fr/files/Piketty2020SlidesLongVersion.pdf
Farmers Fable: Simulation benefits of cooperation, retrieved 12/2019 https://www.farmersfable.org/
Gier, Marc Elsberg, novel, blanvalet 2019 https://gierdasbuch.de/gier.php
## COPYRIGHT
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.
