Question

Karen and Sharon are two prisoners who are suspected of burglary and put in separate cells. Currently, the police do not have enough evidence to convict them of the burglary charge, but can convict them on possession of stolen goods. The police place them in separate cells and try to obtain a confession from one or both of them.

If neither Karen or Sharon confess, they'll get the lesser charge of possession of stolen goods, therefore getting a sentence of 1 year. However, the police offer each prisoner a deal: if you rat out your partner, you get zero years in jail and the partner gets 10 years. If both prisoners confess, they will each get 8 years. The police tell the prisoners they are offering their partner the same deal, but the prisoners are separated and can't communicate.

Use the information provided to draw a payoff matrix for this dilemma.

Answer 1

1,1	0,10
10,0	8,8

In this case with two suspects of burglary and being investigated in two separate cells and being given the information about their punishments and offers, the dilemma for their payoff matrix would look like the above given payoff matrix. In which, they both can refuse to confess and can both face 1 year imprisonment, or they can rat their partner out for their freedoms at the cost of their partner's 10 years imprisonment, or they can both confess and get 8 years of imprisonment for both of them. So in this dilemma, the prisoners would hesitate to confess as there is a possibility and if one confesses but the other doesn't to rat their partner out for their freedom, so, this seems very less packable by any of them. Also, if they both confess, it would lead to 8 hears imprisonment for each of them. So, the best alternative for them would be to refuse to confess by both of them and face 1 hear I imprisonment rather than spending 8 hears or 10 years in prison in greed of their absolute freedom. So they would end end up at 1,1.