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







Related Discussions:- Prisoners dilemma, Assignment Help, Ask Question on Prisoners dilemma, Get Answer, Expert's Help, Prisoners dilemma Discussions

Write discussion on Prisoners dilemma
Your posts are moderated
Related Questions
Does neuro marketing give impetus to new consumer behaviour

What is the Vertex Form for a Quadratic Equation ? The vertex form for a quadratic function is as follows: f(x) = a(x - h) 2 + k The graph of this function Is a parabola whos

The curve (y+1) 2 =x 2 passes by the points (1, 0) and (- 1, 0). Does Rolle's Theorem clarify the conclusion that  dy dx  vanishes for some value of x in the interval -1≤x≤1?

A telephone dialled is numbered 0to9. if 0is dialled first the caller is connected to the international exchange system.find the number of local calls that can be rung if a local n


pam bought a new bedroom suit for $2588.she me a down payment of $188 and paid the remaining amount in 24 equal monthly payments .how much did she pay for each monthly payment.

THE MULTIPLICATION ALGORITHM :  Some Class 3 children in a nearby school had been taught the standard multiplication. Algorithm, and had even done reasonably well in the tests bas

how do you add all the Y.AND X UP WITH 3

Lines- Common Polar Coordinate Graphs A few lines have quite simple equations in polar coordinates. 1.  θ = β We are able to see that this is a line by converting to Car

limit x-a/|x-a| equals x-a [a]a [b]0 [c]-a [d]none 0f these