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Table 2.2: Tragedy of the Commons in a Game Theoretic Framework
Strategies B does not add to herd B adds to herd
A does not add to herd (0,0) (-3,1)
A adds to herd (1,-3) (-2,-2)
If both herdsmen decide not to increase the size of their herds then no further cost is
imposed on them and the pay-off from their decision is 0 for both of them. If only A
decides to add an extra head to his herd, then he is a net gainer: Value of extra
output from the cattle added - Value of output lost from the existing herd = 4 - 3 = 1.
B’s loss is greater as he has to bear a cost in terms of reduced output of his existing
herd (-3), but is not compensated - like A - by an increase in his herd size. So his
net loss is : 0 - 3 = -3. An exactly symmetrical picture is obtained for B adding to his
herd, while A maintains a constant herd size - B’s payoff is 1 and A’s payoff is -3.
Finally, we consider the case of both herdsmen increasing their herds. In that case,
each gains 4 from the extra output of the added cattle, but looses 6 from the reduced
output from his existing herd as a result of the increase in size of herd of both (3 + 3
= 6). The net loss, therefore, works out to be -2 for each of the two herdsmen.
Obviously, in this case the total loss to the grazing area is greatest.
It is easy to see that the strategy of adding to one’s existing herd dominates the
strategy of not doing so. In the absence of collusion or coercion, both herdsmen will
choose to increase their herd size even though the consequent over-grazing
adversely affects both of them - which would not have occurred if both of them had
practised mutual restraint.
Section 2.2: Co-operation and Iterated Game Theory
Latter developments in the field of game theory have allayed fears over the
pessimistic conclusions arising out of the PDG structure. They have shown that
extension of the period of the game to an infinite time horizon, or over a finite but
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