Answer Happy

Publish or Perish: Imagine that any newly minted Ph.D. who starts a tenure- track assistant professor job (player 1) is one of two types: high-ability () or low-ability (OL), where Op > L > 0. The assistant professor knows his type, but the department that hires him (player 2) knows only that he has high ability with probability p<1. The assistant professor first chooses how hard to work, which is effectively how many papers to publish in period 1 (the pre-tenure 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 vi(9,1 %) = V - $, where V is the value of being tenured. The department's payoff is lifit tenures a high-ability type and lif it tenures a low-ability type. If the department denies tenure, it gets a payoff of O and the assistant professor's payoff is viq, NIC)=-4. Denote by (g) the department's belief that the professor is a high-ability type given that he published papers.
C. Characterize the perfect Bayesian separating equilibria using the pa- rameters of the game. d. If there is more than one separating perfect Bayesian equilibrium, what is the smallest number of papers that an assistant professor needs to publish in order to get tenure?