Ilyas wrote: It is a psychological question not a statistics quiz.
Sachin4islam wrote:I think both should remain silent as in this case imprisonment is for only one month. If any one opens his mouth against other,the other suffers a year imprisonment and simultaneously their secrets are exposed which would be against interest of both of them.
Statistics: Average of imprisonment......... In first case six months,in second case one month and in last case three months.
Ilyas, well it is mathematical, but it is psychological in the sense that the correct answer depends on what the other prisoner is most likely to do.
Both prisoners are best off, on average, if they do as Sachin suggests and remains silent. The trouble is, how do you know whether the other prisoner will be silent or not, he is in another room, and the police will not tell you what he has done?
This is actually a game played by computers sometimes, and the strategy that usually does the best in this game is a very simple one called 'Tit for Tat'.
'Tit for Tat' always does the same thing. The first turn when it plays the game with another computer (or a human opponent), it will be honest, or silent. On all other turns, it will do whatever it was that it's opponent did in the last turn. If the opponent was honest, 'tit for tat' will be honest, if the opponent betrayed, 'tit for tat' will then betray.
There are a couple of small variations on 'tit for tat' that will improve it's performance somewhat. One is 'tit for two tats', in which the opponent must betray twice, before the 'tit for tat' player will betray. This eliminates the problem of the two opponents getting caught in a never-ending fight of always betraying, by assuming that a single betrayal might be an accident or confusion. Another variation that does better is 'forgiving tit for tat' in which the 'tit for tat' player will sometimes be honest, even when it has been repeatedly betrayed, which accomplishes much the same thing, it gives the opponent another chance to be honest, and is a way out of an otherwise never-ending fight of always betraying.
There is one strategy that SOMETIMES does better than 'tit for tat', in these games, but it sort of cheats to do so, this is the 'master-slave' strategy, in which two players who know eachother, and have previously agreed to do so, will have one player (the slave) always remain silent, and the other player (the master) always betray the slave. This lets the 'Master' player get very high scores in the game, higher than 'tit for tat' players, but it means that the 'slave' gets very low scores.
On average, the scores of a group of 'tit for tat' players (or the variations of 'tit for tat' I mentioned) is much higher than a group of 'Master-Slave' players in this game. 'Tit for tat' is also a better strategy for real life, such as the two prisoners I described who were actually arrested by the police, it would be a wretched way to treat someone to make them really play the part of the 'slave' and go to jail for a long time so that the other person could get off completely free.
