6. Consider the following game 2 1 U 3 C M D X C, 2 3,5 5,1 Y 3,1 4,2 2,2 N 3,3 2,1 5,4 (a) Characterize the set of rationalizable strategies in this game as a function of C.
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- 6) The following is a static game D 2,2 0,3 D 3,0 1,1 a) Convert this game into dynamic form game b) Find the Nash equilibrium and subgame perfect Nash equilibrium of this game. c) If you consider this game as dynamic then what kind of dynamic game is this.Consider the following sequential game: 1 O D,L U.L U,R U D,R D (0,2) 2 L What is the subgame perfect Nash equilibrium of this game? R. (-1,-1) (1,1)Consider the following normal form game Player 2 L C R Player 1 U 5, 4 4,5 3,8 8,3 8,0 5,5 6,3 0,8 M D 8,8 Find all the pure strategy Nash equilibria of the game.
- 2. Consider the following game: u 1 r 6,0 0,6 d 3,2 6,0 Are there any Nash equilibria in pure strategies for this game? Find the mixed strategy Nash equilibrium.Consider the game R T 11 1.0 10 M 014.0 0.1 B 0.10. 4.0 (a) Find the Nash equilibrium in pure strategies. (b) Find the Nash equilibrium in completely mixed strategies. (c) Find the Nash equilibrium in partially mixed strategies ove the support {A. B} x {C.R).3) Consider the following two extensive form games and answer the following questions. How many subgames present in the following games? Find all pure strategies SPNE. Find all pure strategies NE of these games. Game A Game B u (5,3) u (0,2) 2 2 L L (-5,4) d (0,0) 1 1 1 (1,-5) (-10,-10) u R (2,3) A M 2 R 2 r d 1 (8,1) B (2,0) (2,2)
- Question 5 Consider the following Extended Form Game: A' (1,1) A P2 B' O [(B, B')} (2,3) O ((B.(B',A')). (B.(B¹, B'))) P1 A' What is the set of Nash Equilibria? O {(B.(A', B)), (B,(B', B'))) (4,5) B O ((B.(A'A')). (B.(A, B')). (B,(B,A')), (B,(B', B'))} P2 B' (6,7)1) Consider the following game. 1 \ 2 A B D 4,2 2,2 5,1 E 4,1 3,5 7,3 F 5,2 4,4 7,0 G 5,4 0,4 3,0 a) Given that o2 = G), 4 find BR,(02) '6' b) Find the set of rationalizable strategies profiles, R of the game. c) Find the pure strategy Nash equilibria of the game1. Consider the following simultaneous move game Player 2 C D Player 1 A 4,3 4,-2 B 2,2 3,-1 C 3,0 4,0 C) Find the pure strategy Nash equilibria.
- Consider the following dynamic game: A (2,0) M 2 K (3,1) B 1 (1,4) A R (5,2) 2 K 1 C (3,1) (2,5) (1,0) (a) What is the strategy set for each player? How many strategies does each player have? (b) Find SPNE. (c) Is there a NE in which action C is a part of equilibrium strategy? (d) Give an example of some other NE that is not SPNE.3. Nash Equilibria Consider the following (normal-form) game. Compute a Nash Equilibrium of this game. U C D L | M R 5,0 1,3 4,0 2,4 1,4 3,5 0,1 1,0 5,0Consider the following sequential game: D 1 (0,0) R D 2 (-1,2) R d (1,1) how to write this game in normal form r d 2 (0, 3) r (2, 2)