In the off-switch problem (Section 16.7.2), we have assumed that Harriet acts rationally. Suppose instead that she is Boltzmann-rational, i.e., she follows a randomized policy that chooses action x with a softmax probability: 

a. Derive the general condition for Robbie to defer to Harriet, assuming that Robbie’s prior for Harriet’s utility for the immediate action a is P(u).

b. Determine the minimum value of β such that Robbie defers to Harriet in the example of Figure 16.11.

(x) = - eBU.) eBUy) -