A mathematical analysis of the Sleeping Beauty problem

The Sleeping Beauty problem (Elga, 2000; see also Piccione and Rubinstein, 1997) is a philosophical dilemma related to conditional probability. It may be succinctly described as follows. Sleeping Beauty is put to sleep, and a fair coin (say, a nickel) is tossed. If the nickel shows heads, then Beauty is interviewed on Monday only, while if the nickel shows tails, Beauty is interviewed on both Monday and Tuesday (and given an amnesia-inducing drug between the two interviews, so she does not remember the first interview during the second). In each interview, without access to any additional information (such as the result of the coin toss, or the existence of any previous interviews, or the day of the week), Beauty is briefly woken and is asked to assess the probability that the nickel showed heads. The question is, what probability should she assign to this?