Management Engineering - Game Theory

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GAME THEORY 5 cfu 2022Surname: Name: Matricola: The exam, or the single exercise, will not be evaluated if: ˆThe Last name and name are not clearly written in the right place; ˆThe explanations are not clearly written and contain cancellations.Exercise 1 Given the following bimatrix game, depending on the parametersa; b2R, 0 @(12 ;6) (4;4) (3;5) (3;6) (8;5) (2;7) (a;3) (6;7) (3; b)1 A; 1. nd the best reaction of the rst player to(13 ;13 ;13 ) for everya; b; 2. nda; bsuch that there is a Nash equilibrium with second player playing(13 ;13 ;13 ) , and write the NEp; 3.show that there exista; bsuch that there is a Nash equilibrium with the rst player playing a pure strategy and the second one a mixed strategy where exactly two pure strategies are played with strictly positive probability, and specify the strategies. Answer 1Answer 2 Answer 3 Short explanations 1 ˆ In the boxes only answers; ˆIf the answer is correct, explanations are revised and the score is assigned according to the accuracy of the explanations, if the answer is wrong 0 points are assigned. 2 Exercise 2 Consider the following glove game, with 4 players:ˆPlayer 1 has two right gloves: ˆPlayer 2 has one right glove; ˆPlayer 3 and 4 have a left glove each. 1.Is the game superadditive, convex?; 2.Find the core of the game; 3.Find the Shapley value of Player 1. Answer 1Answer 2 Answer 3 Short explanations 3