Working Towards A Prisoner’s Dilemma Solution

For those without knowledge, prisoner’s dilemma is basically this: there are two men in prison and they both worked together in a bank robbery but the police don’t have enough evidence to convict them. They are trying to get each of the prisoners to state that the other robber was involved in the robbery and give details. If neither of the criminals say a word, they each serve one month. If one criminal states the other one robbed the bank, that crinimal goes free and the other serves 1 year. If they both tell on eachother, they both get 3 months. The criminals can’t communicate with eachother, they are interviewed separately. What should the prisoners do?

 This is an unsolved problem in game theory. It’s very interesting. This isn’t however a 2 player game. It’s a 3 player game. The two crimininals are the police are all separate entities in this game. That’s akey distinction. In two player games theree is no dilemma, simply do whatever makes the biggest difference between you and your opponent.
 
 Here’s an interesting though experiment I came up with which may help with solving the problem. Suppose there are two people who are exact copies of eachother down to the atom. They are both placed in isolation in rooms with two buttons. One red and one green. If both press the green button both will recieve $1000. If one of them presses the red button and one presses green, the player who pressed red gets $5000. If both press red both get $0. What action should be done?
 
 The most important concept in play is that whatever button one person presses, the other must press two because they are exact duplicates of eachother. If one person has a given though process the other must have it too. Keeping this in mind, both players know that if they press red, they will both press red and if they pick green they will both press green. There is no scenario where one presses red and one green. This makes the solution rather simple: press green.
 
 Even though each player knows that the other player is pressing red, this is not sufficient justification for switching to pressing red in an attempt to exploit the other person because the other player will jump to the same conclusion.
 
 Now what would happen if the subjects were exact copies of eachother except for one atom? They both knew this. What should their actions be? They should both press green again. But there is a non zero probability that one presses red and the other green becauuse that 1 atom difference could change how a person reasons about the buttons and how he ultimately makes that choice. It’s incredibly unlikely.
 
 What about 2 atoms? And 3? As the differences in each player increases, the reaoning we used that the other person must do the same as us becomes weaker and weaker. Is it therefore more likely that both players press red as the differences between them increase. Essentially there is little guarantee that the other player will not betray them in a grab for the most money.
 
 One might think “Ah, the opponent thinks I’m very similar to him but I’m not so he will press green and I will press red”. This strategy would work. If one player thinks he is similar to the other, but the other does not think he is similar to the other, the player who thiks he is dissimilar would come out victorious on some occasions.
 
 If you know you are going to be in a situation like this, before going into the scenario instead of saying “press green” (that will be of little use) try to convince the other person that you aree very similar to him and think like him. This will allow you to press red when he presses green.
 
 This may go towards explaning why similar people trust each other more than disimilar people. There are many every day scenarios which are analogous to prisoners dilemma.
 
This sort of reasoning applies when there’s only just 2 players. Supose you live in a flat with a housemate who is similar to you. When a person leaves the flat they will leave their wallet with lots of money in at the flat. It would be easy for the other person to steal the wallet and get away with the crime. So why isn’t it done? Because it implies that the other person would have sloten their wallet. I must remind you that free will does not exist. The house mates are bound to act similarly to each other as a result of being similar. Thinking of the situation in a vaccuum is impossible. You can’t just observe the situation until one housemate leaves, then say “a rational actor would steal the wallet”. It is essentially that causality goes backwards in time. By stealing the wallet, you make it more likely that in the past your wallet was also stolen without your knowledge. Even if you have perfect knowledge of the past and know your wallet was not stolen, you can’t think of it like this because the reason it was not stolen was because it was determined that in the future you would not steal his wallet because he didn’t steal yours. You can’t go against this calculation of the future that was done if it was accurate. It’s binding. Free will doesn’t exist – you can’t use it to escape predictions of the future.

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