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 th... (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 th... (read more)