Describe in words (no maths!), as completely as you can, but also in a concise way, what would happen in a separating equilibrium to this game (in which you can distinguish between both types). There are two pooling outcomes of this game (in which you cannot distinguish between both types since they do the same). Again describe completely, but concisely, what those two outcomes would look like. Now please do the math. What is the set of possible N that will accomplish your task of screening the Brilliant types out from the merely good ones?
Suppose you are Dean of the Faculty at St. Anford University. You hire assistant professors for a probationary period of seven years, after which they come up for tenure and are either promoted and gain a job for life, or turned down, and must find another job elsewhere.
An assistant professor’s type is either Good or Brilliant. All worse types have already been weeded out in the hiring process, but you cannot distinguish between Good and Brilliant types. An assistant professor observes his/her type, and you would like to only tenure Brilliant types.
Consider that the total lifetime payoff of being tenure at St. Anford is $2 million, while anyone denied tenure at St. Anford will be hired by some College and receive a lifetime payoff of $0.5 million.
Tenure decisions are entirely based on scientific publications. This requires doing research and publishing the findings. Each publication requires effort and time and causes strain on the family; all these are costly to the faculty members. The monetary equivalent of this cost (for one publication) is $30,000 for a Brilliant type and $60,000 for a Good one (think of it mainly as
- Describe in words (no maths!), as completely as you can, but also in a concise way, what would happen in a separating equilibrium to this game (in which you can distinguish between both types).
- There are two pooling outcomes of this game (in which you cannot distinguish between both types since they do the same). Again describe completely, but concisely, what those two outcomes would look like.
- Now please do the math. What is the set of possible N that will accomplish your task of screening the Brilliant types out from the merely good ones?
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