Management Engineering - Game Theory

Full exam

GAME THEORY 5 cfu February 4 2019Surname: Name: Matricola: Exercise 1 Given the following game, where Pl3 chooses the matrix(3;0;7) (1;4;2) (2;1;0) (3;4;5)  (40;1;9) (0;4;4) (9;1;40) (a;4;0) 1.Reduce the game by eliminating strictly dominated strategies; 2.Find all NE in pure strategies for everya2R; 3.Find all NE for everya6 = 0. Answer of exercise 1 1.The second column strictly dominates the rst one in both matrices, thus for PL2 is strictly dominant to playsecond row. 2.From before, the game reduces (with Pl3 as column player) to(1;2) (0;4) (3;5) (a;0) From this we see that(3;5)is a N.E. outcome and(0;4)is another NE ia0. 3.Ifa >0, the second row strictly dominates the rst one, and thus(3;5)is the unique NE. Ifa