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## NetLogo User Community Models

# coinGame1

## 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

Players in the form of turtles (yellow circles) sit on a plane. Their vertical position reflects the actual wealth, the horizontal position is the turtle's number.
Lorenz Curve, Gini Coefficient and a histogram show the current distribution of wealth.
You can explore the intrinsic effects of "the rich get richer" obscured by the misleading ergodic hypothesis in traditional economics and the benefits of cooperation induced by a form of wealth-tax.

## HOW IT WORKS

"anz-turtles" turtles play the coin game. Each of them throws a coin at each tick:
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 thru risk-sharing between players.

## HOW TO USE IT

Use the sliders to control the number of turtles "anz-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 all).
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.
Optional set "tax-factor", "tax-limit", and "redist-all?"
If you want bancrupt turtles to die, set "turtles-die?" to on, then 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 black world area. The vertical position reflects the actual wealth, the horizontal position the turtle's number. 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

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)
Try different "tax-factor"s and "tax-limit"s, switch "redist-all?" on/off.
What effects can you see in the histogram, Gini Plot and Lorenz Curve?

## EXTENDING THE MODEL

better visualization ideas?
correct logic of log10 plot (log abs is a dirty fix for negative wealth)

## 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

## CREDITS AND REFERENCES

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