Game Theory 101   no comments

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The Prisoners’ dliemma
Two theives plan to rob a shop, as they approach they are arrested for trespassing (the story differs depending on where you get it from, but focuses on the same point). Based on the assumption the criminals were going to rob the store they put them in different rooms at he station, giving each the same choice:
‘ in exchange for your cooperation, I will dismess your tresspassing charge, and your partner will be charged to the fullest extent of the law – a twelve month jail sentence… if you both confess, your individual testimony is no longer as valuable and your jail sentence will be eight months each.’

Game theory assesses the game with a matrix, see below:

There are two rows and two columns relating to each of the two criminals. Each players ‘payoff’ is a ranking of his most preferred outcome. In this game we are to assume that the players main intention would be to reduce the time spent in jail. The core of Game Theory is the opinion that everybody is ultimately selfish and will always do what is best for them, when confronted with the option to do so. ‘ Game theory does not force players to believe that this is case, as critics frequently claim’. GT simply analyses the options and assembles the most likely strategy for each player based on the potential outcomes.

The most preferred outcome in this case is worth 0, the least is -12 and everything else is representative to the game being played. These values are irrelevant to the outcome of the game however, as they can be replaced with other sets of numbers such as 1-4 representing the most and least preferred outcomes see below:

We are able to see from both tables that the preferred outcome for both players is to confess. There are more complex tree structures and matrix diagrams to go, but for now this is Game Theory 101.

Written by pmb1g11 on December 7th, 2011

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