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# Rich get Richer vs Wealth Tax.nlogo

Author: Rupert Nagler, Jan 2020, nagler@idi.co.at

## WHAT IS IT?
**"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:
https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf

## HOW IT WORKS

* 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.

## 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 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".

## THINGS TO NOTICE

* 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.

## THINGS TO TRY

* 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?

## EXTENDING THE MODEL

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

## NETLOGO FEATURES

* 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, nagler@idi.co.at. 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.