6. (Prisoner's Dilemmas) An important class of games is called the Prisoner's Dilemma which gets itself name from a book by William Poundstone, where they explain it aslz Two members of a criminal gang are arrested and imprisoned. Each pris- oner is in solitary connement with no means of communicating with the other. The prosecutors lack suicient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultane- ously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is: o If A and B each betray the other, each of them serves two years in prison 0 If A betrays B but B remains silent, A will be set free and B will serve three years in prison (and vice versa) 0 If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge). 1Poundstone, William. Prisoner's Dilemma/John von Neumann, Game Theory and the Puzzle of the Bomb. Anchor, 1993