Game theory: Person A and Person B are awaiting charges for crimes, and are currently in court. If both Person A and Person B testify against each other, they both receive 5 years in prison. If one person testifies against the other, but the other refuses to testify, then all charges will be dropped on the person who testified, and the person who refused to testify will face 10 years in prison. If both persons refuse to testify against his/her cohort, then the court will be unable to determine the culprit and will instead sentence both of them to 1 year each for lesser crimes.

Question

anonymous · Answer

Both persons must now make a decision. Neither are permitted to communicate to each other. What is the optimal decision for person A, given that he does not know whether person B has testified against him or not?

mr.math · Answer

@James, could you let me try first before you answer? :D

anonymous · Answer

Bt                Br
At   -5, -5         0, -10
Ar  -10, 0         -1, -1

mr.math · Answer

He should testify against B.

anonymous · Answer

right

mr.math · Answer

I know! :P

anonymous · Answer

but why is it right? Is it because A could possibly get away scot-free if B refuses?

anonymous · Answer

or will the testify strategy make sure that A won't end up in the worst-case of 10 years in prison?

mr.math · Answer

Assuming B testifies against A, then it's better that A testifies too cuz A would receive 5 years instead of 10. If B doesn't testify, which is the second case, then all charges will be dropped instead of  receiving one year in prison.

anonymous · Answer

right

mr.math · Answer

So, it's better that A testifies against B regardless of what decision B would make.

mr.math · Answer

@agd, Do you know the five pirates question?

anonymous · Answer

gud1