Where do you think our President and VP will end up? Think about either one of them. For simplicity just pick the VP (you can do this the other way around). He would think like this. If he testifies against the President and the President does not testify against him, he will be free. It is better than 1.5 year promised by the evidence, if he refuses to testify. If it turns out the President also testifies against him, he will get 2 years. It is better than 3 years, a consequence if he refuses to testify while the President does testify against him. From these two scenarios, it seems that it is better for him to testify instead of refusing the offer.
Of course you can replace the VP in the above paragraph with the President (or the other way around, depending on what you did above). The logical result will apply as well. That is, it seems better also for the President to accept (i.e. to testify against the VP) than to refuse the deal.
Where does this leave us? Yes, if both of them are rational, they both testify and both will stay in jail for two years. Too bad. If only they can communicate each other, they will end up only with 1.5 years each. Do you see why?
Next time we will see what is going to happen if we put more complexity into the game. Say, what happens if the President is a flip-flop kind of guy and the VP knows this very well. Here's a spoiler: both will 'randomize' their action.
Stay tuned (but what are the odds of me continuing this story?)