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Game theory is the strategy of modeling strategic interactions between problems. Generally regarded as a high-level economics concept, game theory has many implementations in real life. It is used in many fields like psychology and science. Here, a Quoran explains the ABC of the theory.
I think many of the answers here are more high-level. Since the asker seems to want a specific interesting example of game theory, let’s dive into the world of cannibalism.
Here’s the problem:
A traveler gets lost on a deserted island and finds himself surrounded by a group of n cannibals.
Each cannibal wants to eat the traveler but, as each knows, there is a risk. A cannibal that attacks and eats the traveler would become tired and defenseless. After he eats, he would become an easy target for another cannibal (who would also become tired and defenseless after eating).
The cannibals are all hungry, but they cannot trust each other to cooperate. The cannibals happen to be well versed in game theory, so they will think before making a move.
Does the nearest cannibal, or any cannibal in the group, devour the lost traveler?
The first step is to recognize that the traveler is just a tired and defenseless cannibal. Once you do that, the problem can be reduced to one just involving cannibals. To solve it now, let’s take small sample sizes.
Sample Size: n = 1
This is almost a laughably easy problem to solve. If there’s one cannibal, and of course the one traveler, then the cannibal will obviously eat the traveler as he has nothing to fear from any other cannibals.
Sample Size: n = 2
Two hungry cannibals and a defenseless traveler make for a harder problem. Remember that we concluded that the traveler is effectively a defenseless cannibal, and by extension, a defenseless cannibal is merely a traveler.
What the cannibals will probably realize that if one of them eats the traveler, they will become prey for the other cannibal. Therefore, their eating the traveler constitutes their death.
Because of this, neither cannibal will attack and the traveler will be safe.
Sample Size: n = 3
Here’s where the problem gets interesting.
If there are three cannibals and one traveler, this problem can be reduced to one that we have solved before. Assuming that the cannibals are well versed in game theory, they will figure out that the first one to attack will reap the benefits.
What do I mean when I say that? If one cannibal eats the traveler, they become a traveler, and the problem is reduced to n = 2. Therefore, the remaining two cannibals will not attack, and the first cannibal to attack will be safe.
How do we solve this problem, then? If there are an odd number of cannibals, the cannibals will attack; Given an even number of cannibals, they will not attack and the traveler will be safe.
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