Okay, that’s making more sense—the part where you get to parameterizing p as a real is what I was interested in.
But do you do the same thing when applying UDT to Newcomb’s problem? Do you consider it a necessary part of UDT that you take p (with 0<=p<=1) as a continuous parameter to maximize over, where p is the probability of one-boxing?
Fundamentally, this depends on the setting—you might not be given a random number generator (randomness is defined with respect to the game), and so the strategies that depend on a random value won’t be available in the set of strategies to choose from. In Newcomb’s problem, the usual setting is that you have to be fairly deterministic or Omega punishes you (so that a small probability of two-boxing may even be preferable to pure one-boxing, or not, depending on Omega’s strategy), or Omega may be placed so that your strategy is always deterministic for it (effectively, taking mixed strategies out of the set of allowed ones).
Okay, that’s making more sense—the part where you get to parameterizing p as a real is what I was interested in.
But do you do the same thing when applying UDT to Newcomb’s problem? Do you consider it a necessary part of UDT that you take p (with 0<=p<=1) as a continuous parameter to maximize over, where p is the probability of one-boxing?
Fundamentally, this depends on the setting—you might not be given a random number generator (randomness is defined with respect to the game), and so the strategies that depend on a random value won’t be available in the set of strategies to choose from. In Newcomb’s problem, the usual setting is that you have to be fairly deterministic or Omega punishes you (so that a small probability of two-boxing may even be preferable to pure one-boxing, or not, depending on Omega’s strategy), or Omega may be placed so that your strategy is always deterministic for it (effectively, taking mixed strategies out of the set of allowed ones).