1. (professor - TA game) Professor Hahn can give a TA scholarship to Yun for maximum 2 years. At the beginning of each year professor Hahn decides whether he will give a scholarship to Yun or not. Yun can get a scholarship in t=2, only if she gets it in t=1. Basically, professor Hahn and Yun will play the following game twice. Prof. Hahn No scholarship `Give scholarship TA Yun (0,0) Work Don't work (2,X) Y-2,3) Yun can be a Hard working type with probably 0.4 and can be a Lazy type with probability 0.6. Professor Hahn does not know Yun's type. If Yun is hard working, it will be X=5 and Yun will always work if she gets a scholarship. If Yun is lazy, it will be X= 2. There is no time discount for t=2. Find out a Perfect Bayesian Equilibrium of the game