In the original problem you presented (the one without any further crimes), I don't think testifying is always the best option. As Alice, if you are both aware of your mutual rationality and know nothing about each other but that, wouldn't a better option be biased randomization? Consider the probability of Bob testifying against you to be 50% and calculate the optimal probabilities for your decision in order to minimize the number of years in prison (negative utility). You get a 7/13 chance of testifying against him. However, remember the other player is rational and that the game is symmetric, so he will also have the get the same probability as you.... (read more)
In the original problem you presented (the one without any further crimes), I don't think testifying is always the best option. As Alice, if you are both aware of your mutual rationality and know nothing about each other but that, wouldn't a better option be biased randomization? Consider the probability of Bob testifying against you to be 50% and calculate the optimal probabilities for your decision in order to minimize the number of years in prison (negative utility). You get a 7/13 chance of testifying against him. However, remember the other player is rational and that the game is symmetric, so he will also have the get the same probability as you.... (read more)