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A newly minted l'h.D. who starts a tenuretraclc arsistant professor job {player 1] is one of two types: high ability {Hg} or lowability [EL], where H\" } EL ;-- i]. The assistant professor knows his type, but the department that hires him {player 2] knows only that he has high ability with probability p 4:: %. The assistant professor rst chooses how hard to work, which is emtively how many papers [q] to publish in period 1 [the pretenure period). After observing how many papers the assistant professor published, the department decides whether to grant him tenure {T} or not to do so {N}. if the department chooses to grant tenure then the assistant professor's payoff is i:1{q,T|IEij = If g, where if is the value of being tenured. The department's payoif is 1 if it tenures a high ability type and -1 if it tenures a low ability type. If the department denies tenure, it gets a payo' of {'3 and the assistant professor's payoff is ?}1[E',NIH} = . Denote by Fill} the department's belief that the professor is a highability type given that he published I} papers. {a} Write down a \"rough\" extensive form of this game. {h} if there is a pooling perfect Bayesian equilibrilun, will the assistant professor be tenured? Does he write any papers? What then is the unique outcome of the pooling perfect Bayesian equilibrium? {c} Characterize the perfect Bayesian separating equilibria using the parameters of the game. {d} if there is more than one separating perfect Bayesian equilibrium, what is the smallest number of papers that an arsistant professor needs to publish in order to get tenure