Q(3)-(4} Two students are competing for a scholarship. which will he given to the one with better performance. The performance y; of a student 1' is determined by yt- = , where et- is the student's effort. If pl 3:: 312 {F2 \"P F1]I then student 1 {2} gets the scholarship; if y1 = y? then the university uses a lottery to decide the winner; each has 1,52 chance of winning. Let the value of the scholarship he V. The payoff function of student 1 is V E1 if F1 :3 F2 [AM-21,32} 2 E1 if F1 '5: Fa VII? e1 if F1 2 F2 In the payoff function, e1 is the cost of effort to the student. Likewise. the payoff function of student 2 is V '32 if F1 '5: Fa U2l31132l = 32 if F1 3' F2 VIEEa if F1 =F2 Suppose that e.- E [ISLE], 1' = 1,2, where E is the maximal elTort. {3} 1FWhat is the Nash Equilibrium {e3. e5] if e c: VIE? (4} What is the Nash Equilibrium 11 V :1. e :2 W2