Question

Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0) (-1,0) (-1,1) C (0,1) (1,0) (0,2) (0,2) (0,2) A В (0,2) 1,2) (0,2) (0,2) (0,3) (0,4) (-1,3) (0,3) a. Use the Elimination of Weakly Dominated Strategies Criterion to obtain a solution (unique to the chosen order of elimination) b. Show that the order of elimination matters by finding a different solution (unique to the new chosen order of elimination) c. Show that the solutions in (a) and (b) are also Nash Equilibria and that there are more Nash Equilibria in this game

Answer 1

Page 1 a Sor t when comparing for two players we see that I dominated by ll. so after a between 1 and 1 elemination of I we will have (-2,0) Coll) (-1,0) (012) (-12) (012) (012) (013) (012) Cou) (13) Now for player it is dominated by B I (012) (013) (012) (-112) (012) (012) (+13) Now I dominated I 7 (012) Hil) Con) (013) (112) Coru) And domains B ī (012) (013) ID (ou) Now I Dominates I and so sambam D dominates c t is coru) e

Page: ③ When compare and I then I dominats per (-2,0) 2 (-1,0) (012) (-1,2) (014) (01) (012) (012) (-13) A 1012) (013) Now for player IA is dominated by B A (012) c (012) (013) 6 (012) (112) 11 COIH) (012) IL (-1,3) Now I and I, I Dominates (012) TO I (012) (-12) (012) (04) (-1/3) O alow in Band D, B Dominales 1 (012) I - B (012) I c I (-112) (012) Now Between B and C, B Dominates and Eameibrium is (012) @ Now If player I choose then I is the strategy for player • 2 and it player a chooses I first then D&B is the Best stratuay for player iso (ou) and (012) are nash soubyom.

It player I chooses A then toll will be best strateay for players 2 and it player 2 chooses I first then A is one of the best strategy for I so (01) is also a nash Eaucibrium so we see that there are more nash caucibrium. e e