Assignment Problem: Harry, Ron and Hermione are choosing courses for their new semester at Hogwarts. Harry and Ron are interested in the course "Badass Fighting Poses," and Hermione is interested in the course "Magic Economics." However, they prefer taking the same course to taking different courses: Harry and Ron will freeload on Hermione's perfect notes, while Hermione wants to constantly scold them on taking her perfect notes. The payoff matrix is given below. Harry and Ron choose together and they constitute the row player, while Hermione is the column player. Hermione Badass Fighting Poses Magic Economics Harry Badass Fighting Poses 3, 2 k, 1 & Ron Magic Economics 0, 0 2, 3
a. Find all mixed strategy Nash equilibra of this strategic game when k = 1, assuming that the expected payoffs represent utilities.
b. Now Harry and Ron prefer the Badass Fighting Poses course even more, even if they cannot coordinate with Hermione, and thus now k = 2. Find all mixed strategy Nash equilibra of this strategic game when k = 2, assuming that the expected payoffs represent utilities.
c. Interpret the results found in parts a. and b.