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Derfect Bayesian equilibrium

Derfect Bayesian equilibrium

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question 1: Publish or Perish A newly minted Ph.D. who starts a tenure-track assistant professor job (player 1) is one of two types: high- ability (0H) or low-ability (0L), where 0H > OL > 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 < . The assistant professor first chooses how hard to work, which is effectively how many papers (q) 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 v1(q, T|0) = V – %, where V is the value of being tenured. The department's payoff 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 payoff of 0 and the assistant professor's payoff is vi (q, N|0) = -. Denote by µ(g) the department's belief that the professor is a high-ability type given that he published q papers. (a) Characterize the perfect Bayesian separating equilibria using the parameters of the game. (b) 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?
Transcribed Image Text:Question 1: Publish or Perish A newly minted Ph.D. who starts a tenure-track assistant professor job (player 1) is one of two types: high- ability (0H) or low-ability (0L), where 0H > OL > 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 < . The assistant professor first chooses how hard to work, which is effectively how many papers (q) 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 v1(q, T|0) = V – %, where V is the value of being tenured. The department's payoff 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 payoff of 0 and the assistant professor's payoff is vi (q, N|0) = -. Denote by µ(g) the department's belief that the professor is a high-ability type given that he published q papers. (a) Characterize the perfect Bayesian separating equilibria using the parameters of the game. (b) 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?
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