Prisoner’s Dilemma.

An investigative essay on the subject of Prisoner’s Dilemma. The essay shall explores more about the probabilities of the scenarios as they happen.

Will need an introduction on what prisoner’s dilemma is, how it works in a simple scenario, as well as a summary of what’s being discussed to start with. The body will discuss the probabilities of each scenario occurring (one betrays the other, both betrays, both stays silent), but also mainly look into the possible expansion, by having the dilemma practiced on more than two people. The body should culminate in a formula (sequential?) that can generate the probabilities of each individual scenario as more people participate (e.g. 1/4 chances of P1 betraying P2 in a two-person scenario, but an even less chance of P1 betraying both P2 and P3, with no one else betraying, and so on).
Mathematical Exploration – Prisoner’s Dilemma
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Background
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The prisoner’s dilemma focuses on the probabilities of strategic decision making.
Specifically, it is “the study of mathematical models of conflict and cooperation
between intelligent rational decision-makers”.
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Scenario takes place on two captured prisoners, questioned separately and not
granted access to each other. If both prisoners confess, both of them gets penalised
for 2 years in jail. If both prisoners remain silent, both of them gets penalised for 1
year in jail. If only one of the prisoners confess, said prisoner will be set free, and the
other will be penalised for 3 years in jail.
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While it is mutually beneficial for both prisoners to remain silent, some people may
want to confess first and be set free. Strategically, it is up to the prisoners to figure
what each of them is going to do, and if any of them are going to confess before the
other.
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Aim
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In my mathematical exploration, I am going to dive deep into the science of probability,
which is applied in game theory. As with all probabilities, there is always a way to
calculate how many different possible scenarios there are.
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The probabilities may be simple when there are two people involved. The dilemma is
exposed when more people are involved, thereby creating more and more possible
scenarios, similar to adding matchsticks to form arrangements of triangles.
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Plan
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To find out the probabilities involved as I add more and more people, research the
possible instance of iterated events (the dilemma being repeated in another set of
scenarios), and hopefully come up with a viable math formula to calculate the different
possibilities as the amount of subjects grow.