Management Engineering - Game Theory

Full exam

GAME THEORY, Management June 23, 2022Surname: Name: Matricola: Only these papers will be accepted back for evaluation; The exam, or the single question, will not be evaluated if: ˆThe surname (last name) and name are not clearly written in the right place; ˆThe box for the answer either does not contain the answer, or contains answer followed by explanations; ˆThe explanations are not clearly written and contain cancellations. Grades: Exercise 1: 2+2+3+2, Exercise 2: 3+3+3Exercise 1 Given the following bimatrix game0 @(3 ;4) (2;5) (5;2) (2;0) (4;4) (6;0) (1; a) (5;6) (b;8)1 A witha; btwo real parameters: 1. nda; bsuch that the game is a potential game; 2.for everya; b2R nd the best response of the second player to strategy(12 ; 0;12 ) of the rst player; 3. nd all mixed Nash equilibria pro les fora