Section 1. Consider the pepper-eating game in Tutorial 10 Question 3. Recall that a hero loses 5 utils for each pepper he eats, and a coward loses 10 utils for each pepper he eats. The queen is indifferent between hiring and not hiring when Pr(hero) = 0.9, strictly prefers to hire if Pr(hero) > 0.9, and strictly prefers not to hire if Pr(hero) < 0.9. The common prior belief is Pr(hero) = 0.5.
For the next few questions in this section, suppose that the swordsman gains X utils if he is hired. If the swordsman gains X = 26 utils if he is hired, is there a perfect Bayesian equilibrium of the following kind?
A hero always eats 1 pepper.
A coward sometimes eats 1 pepper and sometimes eats none.
If your answer is "yes", please enter the probability Pr(Queen hires | swordsman eats 1 pepper) in the box below. Please round your answer to 3 decimal places (e.g., write 2/3 as 0.667).
If your answer is "no", please enter 0 in the box below.