1. professor - TA game) Professor Hahn can give a TA scholarship to Gong Yi for maximum 2 years. At the beginning of each year professor Hahn decides whether he will give a scholarship to Gong Yi or not. Gong Yi can get a scholarship in t=2, only if he gets it in t=1. Basically, professor Hahn and Gong Yi will play the following game twice.

Prof. Hahn

No scholarship Give scholarship

TAGong Yi

(3,X) (-2,3)

Gong Yi can be a Hard working type with probably 0.3 and can be a Lazy type with probability 0.7 Professor Hahn does not know Gong Yi's type. If Gong Yi is hard working, it will be X=5and Gong Yi will always work if he gets a scholarship. If Gong Yi is lazy, it will be X= 1. There is no time discount for t=2.

Find out a Perfect Bayesian Equilibrium of the game.