1. Consider the following dynamic game D LR C 3 2 P LR C 3,3,2 0,0,0 4,4,0 0,0,1 →1,1,1 Find all the perfect Bayesian Nash equilibrium in pure strategies.
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- 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 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)2: Provide a definition for a Nash equilibrium and then find all pure-strategy Nash equilibria of the following game: Left Center Right Up Middle 1,3 2,7 6,3 2,9 4,4 7,10 Down 3,8 2,5 3,4
- 2. Provide the normal-form expression to the extensive-form game below, and find all pure-strategy Nash equilibria there. Find the subgame-perfect Nash equilibrium then. A B X E Y B A B F t G F G BF B D A 0 3. Find the subgame perfect Nash equilibria (may or may not be unique) in the game below. A B 100 30 F 60 9 5 B 3 5 12 10 60 10 80 10 180 60 200 40Consider 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.1. In the following extensive-form game, derive the normal-form game, and find all the pure-strategy Nash equilibria, subgame-perfect equilibria, and perfect Bayesian equilibria. L' M' R' 1 R L M 2 P M' R' 1,3 1,2 4,0 4,0 0,2 3,3 2,4
- 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 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.rock paper scissors rock 0. -3 0. раper scissors -1 -1 3. 0. (a) Show that xT= (,) and yT= (,) together are not a Nash equilibrium 3' 3 3131 for this modified game.
- Consider the following simultaneous move game: Player 1 U M D Player 2 L 2,10 2,5 8,7 C 5,2 11,8 8,4 R 5,4 2,9 8,3 In the Nash equilibrium of this game, player 1 receives a payoff of ✓ and player 2 receives a payoff ofhow many Nash equilibrium/equilibria are there in this game? please refer to figure provided3. 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 5,0