Game Theory
----Henry Bradley (Y13)
Whether it be in the actions of enormous multinational companies or simply the everyday choices we make, game theory plays an enormous role in determining outcomes of our decisions. Game theory, is simply defined as the study of strategic reasoning and decision making. In this article I will present 3 problems, which on the face of it look simple, but actually are surprisingly complex due to game theory. The first problem illustrates how game theory can cause individuals not to cooperate even if it would appear it is in both their interests, it is known as the prisoners’ dilemma: There are 2 prisoners (A and B) in separate cell after committing a crime together. The prisoners cannot communicate with each other at all, but they both have a choice, they can either stay silent, or betray their fellow prisoner. They both have to make this choice, without knowledge of what the other prisoner has chosen, but knowing that the other prisoner also has to make the choice. Here is the deal offered to both prisoners
If prisoner A and B both stay silent, they each get 1 year in prison.
If prisoner A stays silent, but prisoner B betrays A, then A will get 10
years in prison, and B will be set free (and vice versa).
If both prisoner A and B betray each other, then both will serve 5 years
in prison. Clearly, it would seem that it would be in both their interests to both stay silent,
and simply serve the 1 year, however this is unlikely to be the case due to game theory incentives to betray. What is likely to happen is that both prisoners betray. The reason this outcome is likely is that both prisoners have an incentive to betray. For example, imagine you are prisoner B, if prisoner A has stayed silent, and you betray, you will be in prison for 1 year less than if you had stayed silent. If prisoner A has betrayed, if you betray you will be in prison for 5 years
Figure 1 – Table of outcomes
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