A microeconomics professor has to decide whether to include game theory in the syllabus for her class. The class is an elective; therefore, students can decide whether or not to enroll. If the student enrolls in a class that has game theory, the professor's utility is 10 and the student's utility is 5. If the student enrolls but there is no game theory, the professor obtains 7 and the student 10. If the student does not enroll, the professor gets utility of 1 if the syllabus includes game theory, and 0 otherwise. Not enrolling always gives the student a utility of 7 regardless of the content of the class. Choices are taken simultaneously. It is forbidden for the student to dr0p the class, or for the professor to change the class content later in the semester. (a) Represent the game in normal form. (b) Find the pure strategy Nash equilibrium/equlibria. Are there any dominant strategies? Explain. (c) Suppose now that the game is played sequentially. The professor has to post the syllabus in advance and cannot modify it later. Represent the game using a decision tree. ((1) Find the Nash Equilibrium using backward induction. How do the equilibrium payoffs in the sequential game compare to the equilibrium payoffs in the simultaneous game