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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 2d-world 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 wealth-tax.
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 "mult-heads" and "add-heads" is added.
If tails are shown, individual wealth is multiplied by "mult-tails" and "add-tails" is added.
After all turtles have thrown their coins and their wealth was adopted, 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 sharing the risk between players.

## HOW TO USE IT

* 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 actual wealth to bet by "leverage" (default: 1.0).
* Set the multiplicative factors "mult-heads", "mult-tails" (defaults: 0.6, 1.5) with which your bet will be multiplied in case of win / loss.
* Set the additive values "add-heads", "add-tails" (defaults: 0.0, 0.0) which will be added to your bet in case of win / loss.
* Optional set "tax-factor", "tax-limit", and "redist-all?"
* If you want bancrupt turtles to die, set "turtles-die?" to on.
* To setup the simulation, press "setup".
* To play one round press "go-1", 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 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.

## THINGS TO TRY

* Try different values for multiplicative growth ("heads-mult", "tails-mult") and additive growth ("add-heads", "add-tails"),
* Compare the wealth-distribution for no multiplicative growth (set both "heads-mult", "tails-mult" to 1.0) to other values of multiplicative growth (eg. 0.6, 1.5)
* Compare the wealth-distribution for no additive growth (set both "heads-add", "tails-add" to 0.0) to other values of additive growth (eg. -0.2, 0.3)
* Try different "tax-factor"s and "tax-limit"s, switch "redist-all?" 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

in-depth 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://gier-das-buch.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.

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