This is almost accurate. You can slightly increase your chances if you say "I will defect, but will take care of your family and give you half my income forever. If you also defect, we will both go to prison and you will be worse off", then don't actually defect - which means you both cooperate! It won't always work, but it did work flawlessly in a show called "Split or Steal", which basically made the prisoner's dilemma a TV show: https://www.youtube.com/watch?v=S0qjK3TWZE8