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I started to learn about game theory just now. I am confused about the prisoners' dilema, when 2 prisoners are given a choice whether to keep silent or rat out the other guy. From what I read, if one rats out the other and the other guy keeps silent, then the ratted out guy will go free, while the other guy serves 10 yrs in prison. But, if they both rat out each other, then they both serve 7 yrs. See more details here: Prisoners' dilema. From what I read, each guy will be confused as to whether he should choose to rat out his friend or not - he wants to be free, but he is also afraid if the other guy rats out him, then both of them will not serve the shortest punishment.

Now the question is :

is all of this payoff-matrix is given to both prisoners? if so, it's just a simple answer, both of prisoners will choose to keep silent (so both of them will serves 2 yrs in jail), why? (because they will think if they rat out other guy, how if others rat out him too? both of them will serves 7 yrs in jail). I know this Prisoners' dilema gives more details than I thought, but maybe I get the wrong idea of this?

Updated : sir, I found an interesting thing after a few discussion with "myself". The dilema that I found from this case, "may" be :

  1. if I rat him out, I may be get free, but how if he rat me too? both of us will serves 7 yrs. (1st dilema)
  2. if I am confessing, hmmm I serves 2 yrs at least not as long as 7 yrs, but omg, he'll get the chances to rat me out, so I will get 10 yrs in jail while he get free, I wont make him happy for this (2nd dilema)
  3. so, what is the best choice for me? (3rd dilema)

better ratting him out or confessing? hmm, if I rat him out, I will get 2 chances (free or same punishment 7 yrs), but if I confess, I will get 2 chances also (same punishment 2 yrs or 10 yrs while others will free, I wont give him a chance to be free). I know!! the best choice is better ratting him out, yeah!!! omg, but it means I wont be free, cause I know he'll think the same too, it will end up both of us ratting each other (7 yrs of jail), haha I know he'll choose to rat me out cause of this, I better to choose to rat him out too. (both of us end up 7 yrs)

so I think in this case 1st and 2nd dilema will lead each guy to the 3rd dilema, which is lead to the conclusion to choose rat each other, and end up 7 yrs.

so I will updated my question to :

are these dilema which mentioned by "Prisoners' dilema" ? if so, it's so easy to end up in the equilibrium state (ignore the 7 yrs or 2 yrs in jail, just called it "same punishment").

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    $\begingroup$ The real "dilemma" in the prisoners dilemma is that no matter what the other guy chooses, you are better off ratting him out. But this means that you are both worse off if you both do what is best for you personally than if none of you do. I have heard it said that many of the problem s we have in the world today (global warming, overexploiting natural resources, etc) are variations on this single idea that everyone are worse off when everyone does what is best for them. $\endgroup$ – Arthur Jul 23 '16 at 11:22
  • $\begingroup$ so, what do you mean is, each prisoners only know if he rat out his friend then he serves no yrs in jail while the others serves 10 yrs? or is there any information other than this? $\endgroup$ – Yagami Jul 23 '16 at 11:28
  • $\begingroup$ In the classical prisoners' dilemma, the only thing the prisoners do not know is what their buddy chooses. They know about all the consequences in all cases. $\endgroup$ – Arthur Jul 23 '16 at 11:35
  • $\begingroup$ srry to be not clearly in my question, due my lack of english to express my confuse, and because I just start this out right now, so can you explain what kind of dilema you get from this case, if you were the prisoners? cause I myself think, if I were one of this guy, I just simply choose the confessing one (assuming my friend not that stupid to rat me out, cause he will think, that I can rat out him too, so we'll end up 7 yrs), and it's not called dilema I think, I dont think 'simple dilema' can be classified to this 'prisoners dilema'. I assume there is more 'dilema' that the problem gives $\endgroup$ – Yagami Jul 23 '16 at 11:39
  • $\begingroup$ @Yagami, Perhaps you are confusing the words "dilemma" with "paradox". There is no paradox; a dilemma is , according to Wikipedia "A dilemma ...is a problem offering two possibilities, neither of which is unambiguously acceptable or preferable. " $\endgroup$ – nomadreid Jul 24 '16 at 14:54
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Prisoners' dilemma is an example of Nash equilibrium, in which (1) each player of a game knows the payoff from each of his moves, given the other players' moves. In other words, all players know the payoff matrix. And (2) each player of the game plays a "best response" - a well-defined term. Basically means you play to maximize your own payoff, given all other players' moves. See Rubenstein's book on game theory for a reasonably accessible explanation.

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Each prisoner is given the table of payoffs, but neither is allowed to know what the other one has answered. Therefore, because prisoner Alice can reason that, if prisoner Bob guesses that Alice will be silent, then Bob will rat, thereby gaining the best outcome for himself, and the worst outcome for Alice. Bob will reason the same way. Therefore, neither one of them will stay silent, and both will rat, ironically ending up with a bad result for both of them. But both ratting is the Nash equilibrium, where if one changes his/her position (while the other one stays fixed), he/she will only worsen his/her situation.

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    $\begingroup$ There is no need for them to reason in this way. In the prisoner's dilemma each player has a strictly dominant strategy (to confess), i.e. no matter what the other player does, confessing gives a higher payoff. $\endgroup$ – smcc Jul 23 '16 at 11:30
  • $\begingroup$ yes, that is what I mean, if I were the Alice or Bob, I can assume my friend is not that stupid to rat me, cause I assume "he assume the same as me", so better to choose the confessing one, cause I know the other guy will choose the same too, due to the thought of "if I rat him, how if he rat out me too? we will receive the worst yrs, I know my friend is not that stupid, and I know that he know me not that stupid too" $\endgroup$ – Yagami Jul 23 '16 at 11:36
  • $\begingroup$ By confess here I meant the same thing as ratting out. $\endgroup$ – smcc Jul 23 '16 at 11:53

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