charlie brown,
Correct. What you are describing is known as ‘strategic dominance’ in game theory. One startegy (in this case defecting to the prosecution) is better for one player regardless how the player’s opponent might play.
Ironically this is true even though each player’s individual reward would be greater if they both played cooperatively i.e. both remained silent and received a 6 month sentence, since with both acting in their rational best interest (startegic dominance) they both decided to defect and both ended up with a 5 year sentence.