How to selfishly choose the worst result. Rational thinking leading to irrational results: Prisoners Dilemma and similar game-theories

The prisoner dilemma is from game theory which is based on mathematics and on rational thinking, leading to the result that the  prisoners are pitted against each other in simple choices and, individually, make the choice to get a worse result than another possibility.

To put numbers and explanations to the theory: You have two people who have commited a crime, leading to their arrest. However, lacking proof and an admission of guilt, the two Prisoners can only be put into prison for a minor crime. So instead, they each get an offer individually, seperated from each other: If they are the ones to throw the other prisoner under the bus by admitting guilt and blaming the other, they can get immunity from the law for the particular crime, while the other will be punished harshly.

This covers three of the four possible outcomes: If both Prisoner A and Prisoner B hold tight and do not talk about their crime, they get a minor punishment. If Prisoner A talks, Prisoner B will be put into prison for a long time while Prisoner A walks free. The same happens in reverse if Prisoner B talks while Prisoner A refuses to cooperate with the police constable.
So far, the rationale of the criminals would go somewhere along the line of such: “This is a good deal. If i am the one left in prison while my fellow felon talks, i will be staying here a long time: i should instead cooperate and see that i am the one walking.”

However, there is a fourth outcome: Both of them decide that they would like to be the ones to talk. While their admission of guilt in the crime makes the prison-sentence lighter than if they were the ones who were framed for the whole crime, they both will be found guilty and punished harshly.

In numbers for the sake of our math:
Outcome 1: Prisoner A and Prisoner B do not talk: Both are sentenced to 1 year in prison.
Outcome 2: Prisoner A talks and Prisoner B does not talk: Prisoner B is sentenced to 10 years prison while Prisoner A goes free.
Outcome 3: Prisoner B talks and Prisoner A does not talk: Prisoner A is sentenced to 10 years prison while Prisoner B goes free.
Outcome 4: Both Prisoner A and B talk: Both are sentenced to 8 years in prison.

When we watch the (overblown) numbers, our first thought is that there is a substantial wrong in this: If both were to be silent about their crime, they would be put into prison for (together) 2 years.
If one of them talks, they (albeit lopsided) serve in prison for 10 years.
But if both of them talk, they suffer a combined 16 year prison-sentence.

So what is the trap? The Dilemma is that both of them only have a choice of “admit” or “do not admit”. They have no chance to  communicate after the fact. Instead, cold logic gives them two choices with different outcomes.
If they do not talk, they can go to prison for either 1 or 10 years, depending fully on the other ones choice.
If they do talk, they can either fully go free or get an 8 years prison sentence, depending, again, fully on the other ones choice.
And that is where the trap lies: In the mind of any being who has mastered math to the most basic degree: 1+10 = 11, which is a greater number than 0+8 = 8. Even more so, to admit guilt is a more favorable outcome, for ones own person, either way: If their companion is the one who is silent, they go free. If their companion talks about the crime, they “only” are put away for 8 years in prison instead of 10 years. It seems the logical choice.

The Dilemma of the prisoners (or players) lies in the unknown of the behaviour of the other one. The game theory works with the optimal strategy of the prisoners dilemma. The optimal strategy for both would be to trust in each other and cooperate (with each other, not the police). But, after the logical math of the dilemma, we end up that the “logical” behaviour for the two Prisoners would be to  prattle on each other.
“The Strategy of Conflict” by Thomas Schelling goes into the problems of this by aligning it to the conditions of the Cold War: The punishment of not trusting or loosing the trust of the other side would have been so drastical that no one would “win”.

How can you establish the trust necessarry to break the cycle? There are two main theories which would get people to react differently than the established norm. However, both of these theories break our regular scenarion:
1. Repetition of the game: By repeating the game several times, both players would find out that cooperation and unconditional (a key- word in this case) trust in each other is the most assured way to “win” the scenario (by loosing less and cooperate with repeated success).
2. Communication: If the two prisoners were allowed to talk to each other, they could persuade each other in order to come to the right conclusion. Of course, this is not a sure-fire way: A last-moment backstab is possible. However, the proximity and the communication  would lower the chance of an earnest attempt to get away free at the cost of another humanized being.

In part, those two scenarios have been established by a game show from the early 2000’s called “Golden Balls”. In this, two players  were, in the end, put at the position to choose between “Split”, meaning to split the sum of money evenly amongst them, or “Steal”, where the other person is left with nothing.
The catch being that if both were to use steal, nothing would be paid out. Both players would sit across a table and attempt to persuade each other that they are going to cooperate and not attempt to make a grab for the money. However, something weird occured at one of these games. A player named Nick did persuade the other player that he would use steal either way and persuaded his counterpart that he would split the money after the show. This particular game of psychology caused a lot of strife initially and it may be some of the most entertaining 3 minutes of the whole show, culmunating in Nick persuading the other  that he would steal the money, causing the other to choose split…. and then having chosen split himself, sharing the money evenly by the rules.
However, we must be made aware that this is not a “pure” prisoners Dilemma. The addition of the communication and the beforehand- established math is different enough to make it a similar, but not pure game.

So how can the selfishness be broken? With the game-theory having established “selfish” win, it can, mathematically, not be broken.
However, it can be broken by willingness to trust into each other unconditionally.