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tragedy of the commons v4_2

by Young Joon Oh (Submitted: 06/11/2014)

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## TRAGEDY OF COMMONS MODEL By Young Joon Oh

This model is made in Nov. 2 . 2010 by Young Joon Oh at UT Dallas

## INFORMATION

Definition :

When actors >= 2 and they should share the resource, they abuse the resource because of actors' selfishness. In the end, the resource gets exhausted.

Once the common has begun to be destroyed, it gets worse not only in the collective level, but in the individual level.
Reducing the common causes to decrease the Grass (in this model). As a result, sheep's health also become worse.

To solve this problem, collective action is needed.

## EXPLANATION

Assumption :
1 tick = 1 day, 1 year = 360 ticks, a sheep's survival needs 360 energy for 1 year.
A sheep's initial energy = 35. 35 is basic energy for sheep.
A sheep's gestation period = about 5 months. So, if a sheep has 150 energy, it is regarded the sheep is well health conditin. So, a criterion for ideal health condition will be 150.

For simulation of Tragedy of Commons(ToC), it is very important to depict some factors as follows ;

(1) Re-growing grass

(2) Generating and Consuming Energy of Sheep and Grass

(3) Selfish Shepherds

For (1),
Dr. Manske's paper indicates it takes about 4 months for full-grown grass on average.
I assume there is a common with full-grown grass.
So, in this model, Green Grass has 120 green-rate(energy) initially. If the green-rate is exhausted, it re-grows after 240 ticks(i.e. 120+240 = 360).
Thus, even though the energy is not exhausted, the grass begins to re-grow after 240 ticks.

For (2),
If a sheep gets to a grass, the sheep can get 3 units of energy, and the grass lose 1 unit of green-rate. However, the cumulative energy of sheep is 2, because it should consume 1 unit of energy to get to that grass.

So, if a sheep's cumulative energy = 360, it means the sheep already has enough energy to live for 1 year. From 360 to the basic energy,35, the sheep do not need to get more energy from grass. This is called 'Full'.

For (3),
Shepherds want to bring more sheep to the common, when some conditions are met.

First,
all sheep's energy in the common > sheep's health criterion (like 150).
It means all sheep he brought become very healthy. So, it is an incentive for a shepherd to bring more sheep for their health.

Second,
energy of grass (green-rate) > sheep's health criterion.
It means there is sufficient grass in the common to feed extra sheep, without worsening health of the current sheep in the common.

When 'regulation' is operated, the whole common will be divided by 4 parts.
Each kind of sheep can have own part of the common. After that, shepherds have just considered amount of grass in his own part of the common, not in the whole common.

## HOW TO USE

- Input - number : the initial number of each sheep

- Slider - criterion : the criterion of healthy sheep

- Switch - bring-new : if on, the shepherds can bring new sheep

- Switch - sheep-y, sheep-b, sheep-r : if on, yellow, blue, and red sheep will appear

- Switch - regulation : if on, each kind of sheep can be fed on its own grasses
For white, north-west
For yellow, south-west
For blue, north-east
For red, south-east.

## REFERENCES

Llewellyn L. Manske, Grass Growth in Height, http://www.chaps2000.com/bin/ch2r3.pdf

http://www.sheep101.info

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