Simulation of a multiplicative coin game in NetLogo
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.This is a NetLogo model simulating a coin game based on multiplicative growth.
To simply run this model click:
https://netlogoweb.org/web?https://dl.dropboxusercontent.com/s/brtpecs53p216fp/Throwing%20Coins%20-%20Inequality%20and%20Tax.nlogo?dl=0
To start press "setup" and then "go".
To download this model and run with locally installed NetLogo:https://dl.dropboxusercontent.com/s/brtpecs53p216fp/Throwing%20Coins%20-%20Inequality%20and%20Tax.nlogo?dl=1
(recommended for best performance)
http://ccl.northwestern.edu/netlogo/models/WealthDistribution.
Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
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.This is a NetLogo model simulating a coin game based on multiplicative growth.
To simply run this model click:
https://netlogoweb.org/web?https://dl.dropboxusercontent.com/s/brtpecs53p216fp/Throwing%20Coins%20-%20Inequality%20and%20Tax.nlogo?dl=0
To start press "setup" and then "go".
To download this model and run with locally installed NetLogo:https://dl.dropboxusercontent.com/s/brtpecs53p216fp/Throwing%20Coins%20-%20Inequality%20and%20Tax.nlogo?dl=1
(recommended for best performance)
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?
RELATED MODELS
http://ccl.northwestern.edu/netlogo/models/WealthDistributionCREDITS & REFERENCES
Credit: computation of Lorenz Curve and Gini index copied from: NetLogo Wealth Distribution model. Wilensky, U. (1998).http://ccl.northwestern.edu/netlogo/models/WealthDistribution.
Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
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