Game theory
If you are a prisoner in this situation and you only care about yourself, the way to get the smallest sentence is to betray the other prisoner. No matter what, you get a shorter sentence when you betray than when you do not. Imagine a situation where you are one of the prisoners, if the other prisoner stays silent and does not betray, then betraying means you do not go to jail at all instead of going to jail for 6 months. If the other prisoner betrays, then betraying lets you go to jail for 2 years instead of 10 years. In short, "betrayal" is the best strategy, and is called the "dominant strategy."