You might be interested in this paper by Wolfgang Spohn on auto-epistemology and Sleeping Beauty (and related) problems (Sleeping Beauty starts on p. 388). Auto-epistemic models have more machinery than the basic model described in this post has, but I'm not sure there's anything special about your example that prevents it being modeled in a similar way.
You might be interested in this paper by Wolfgang Spohn on auto-epistemology and Sleeping Beauty (and related) problems (Sleeping Beauty starts on p. 388). Auto-epistemic models have more machinery than the basic model described in this post has, but I'm not sure there's anything special about your example that prevents it being modeled in a similar way.