Here we consider a simple game called the Prisoner\'s Dilemma. Two members of a
ID: 3202372 • Letter: H
Question
Here we consider a simple game called the Prisoner's Dilemma. Two members of a criminal gang, A and B, are arrested and are under investigation. Police don't have enough evidence, which makes them long for the prisoner's confession. Criminals have a choice to confess (C) or to deny (D). To encourage the criminals to confess, police offers a bargain: If A and B both confess, each of them serves 2 years in prison If A betrays B(A confesses, B denies), then A will be set free while B will serve 3 years in prison (and vice versa) If A and B both remain silent, both of them serve 1 year in prison What is the sample space in the Prisoner's Dilemma? A decides to confess and betray B. B is reluctant to betray A. Therefore, B is thinking of confessing with a probability of 0.4. (B does not know what A will choose and vice- versa) What is the possibility of A being set free, and B serving 3 years in prison? What is the possibility of both A and B serving 2 years in prison?Explanation / Answer
Solution for Parts (b) and (c) as requested
Part (b)
P(A is set free and B is awarded 3 years in prison) = P(A confesses and B denies)
= P(B denies) [because we are given A has decided to confess]
= 0.6 Answer[because P(B denies) = 1 - P(B confesses) = 1 - 0.4 (given)]
Part (c)
P(A and B are awarded 2 years in prison) = P(A and B confess)
= P(B confesses) [because we are given has decided to confess]
= 0.4 Answer[because P(B confesses) = 0.4 (given)]