Prisoners dilemma, Mathematics

Prisoners Dilemma

This is a type of non-zero sum game and derives its name from the given story:

The district attorney has two bank robbers in separate cells and offers them a chance of confession. If one confesses and the other does not then the confessor gets two years and the other one ten years. If both confess they will get eight years each. If both refuse to confess there is only evidence to ensure convictions on a lesser charge and each will receive 5 years

Another illustration

The table given below is a pay off matrix for two large companies A and B. initially they both have the similar prices. All consider cutting their prices to gain market share and thus improve profit

Corporation B

 

Maintain prices

Decrease prices

maintain prices

3,3 status quo

1 , 4 B gets market share and profit

Decrease prices

4, 1,  A gains market share and profit

(2,2) Both retain market share but lose profit

Corporation A

The entries in the pay off matrix show the order of preference of the players that is first A then B.

We may assume that if both player study the condition then they will both decide to play row I column I(3,3).

Conversely

Assume A's reasoning is as given below:

I should play row 2 because I will increase my gain to 4, If B plays column I

In the similar way B's reasoning may be as given below:

I should play column 2 to get pay off 4 per play, if A plays row I

If both play 2 as row 2 column 2 each two gets a payoff of 2 only

In the long run pay off forms a new equilibrium point since if either party departs from it without other doing then he will be worse off before he departed from it

Game theory appears to indicate that they should play (2,2) since this is an equilibrium point however it is not intuitively satisfying. On the other hand (3,3) is satisfying but does not show to provide stability. Thus  the dilemma

Posted Date: 2/19/2013 5:42:41 AM | Location : United States







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