This simplified numerical example of the use of common land by commoners to pasture cattle illustrates how the Tragedy of the Commons occurs.

This common land has an optimum stock of ten head of cattle, and there are five commoners with rights to use the common land. Each commoner starts with two cattle on the land.

The cattle are the productive output of the common land, so each commoner, with two of the ten animals, gets 20% (2/10ths) of that productivity.

One of the commoners adds one more animal, so now there are eleven cattle on the common. The commoner who added the extra animal owns three of the eleven cattle that are on the land and now gets 27% (3/11ths) of its productivity. The other four commoners, each with only two of the eleven cattle, get only 18% (2/11ths) of the productivity. The commoner who added the extra animal has increased his or her share of the productivity by 36% (from 20% to 27%); while the other four commoners have had their shares of the productivity reduced by 10% (from 20% to 18%).

So, even though the cattle belonging to the commoner who added the extra one are in poorer condition than they were (as are all of the cattle), he or she has still increased his or her share of the productivity by 36% by adding the one extra animal.

Because the total productivity of the common land will not increase beyond that of its optimum stocking rate, the part of it that goes to the added animal must be subtracted from all of the cattle that are already on the land. The commoner that added the extra animal gets all of the productivity that the extra animal takes from the existing animals, but only suffers some of the consequent loss to the existing cattle, in proportion to how much of the existing cattle he or she owns. Unless he or she owns all of the existing cattle the gain must always exceed the loss, no matter how many animals there are and no matter what damage is done the common land from overuse.

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An example of Tragedy of the Commons 

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