Consider the following game: L R A 7,2|1,3 B 4,14,1 Cl1,57,0 two mixed.strategy Nash equilibria. In one of them, player I plays the strategy 6,-(0,1,0). There are the two equitibria, and both playe's expected what are امام what are payoffs? (Note: This s a tricky problem!)
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- GAME UUU B1 Player B B2 A1 7,13 5, 10 A2 3,8 9,16 Player A A3 5,8 4,7 In Game UUU (see table above), assuming players move simultaneously, Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. Player A choosing A3 and Player B choosing B2 is a Nash equilibrium. Both Player A choosing A1 and Player B choosing B1 and Player A choosing A2 and player B choosing B2 are Nash equilibria in pure strategies Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff ofFind the unique Nash equilibrium of a game with the following payoff matrix: Player 2 2 4 1 (6, 7) (13, 8) (9, 9) Player 1 3 (4, 4) (7, 7) (7, 6) (7, 7) (11, 11) (7, 13) О a. (3, 2) O b. (5, 4) О с. (11, 11) O d. (1, 6) O e. There is no unique Nash equilibrium.
- Help me please2- Consider the following game. Player 2 Player 1 U 12, 2 | 3, 9 5, 8 4, 2 D (a) Find all the Nash equilibria, pure and mixed. (b) Suppose that the payoff of the column player u:(D, L) is reduced from 8 to 6, but all other payoffs remain the same. Again, find all the pure- and mixed-strategy Nash equilibria. (c) Compare the mixed-strategy equilibria in parts (a) and (b). Did this worsening in one of player 2's payoffs change player 2's equilibrium mixed strategy? Did it change player l's? Give some intuition.Consider the following two player extensive form game. メ (2,5) (4,) (3,5) a. Find the induced normal form of the given extensive form game using the pure strategies of the players. Find out all the possible Nash Equilibrium of this game. b. From the Nash Equilibrium you are getting in part a., which one is subgame perfect Nash Equilibrium? Explain with appropriate reasons. c. Explain why the NE in part b. is credible. (Use maximum 3 sentences):
- 15) Find all Nash equilibria (both pure and mixed strategy) in the following game Player 2 Left Right Player 1 Up 10,8 0,5 Down 4,0 3,6Consider the two-player game depicted below w А 1,5 2,2 0,4 3,11 В 13,0 4,1 2,5 4,2 с 1,3 2,6 5,2 2,0] a. What is Player 2's best response if Player 1 plays B? b. What is Player l's best response if Player 2 plays z? c. What are the pure strategy Nash Equilibria? సా5 Suppose two players play one of the two normal-form games shown in Figure 1. L U 0,-1 D 2,4 R 2,0 6,0 L U | 4,-1 D 2,-2 R 2,0Now suppose that Player 2 knows which game is being played, but Player 1 does not. Find the pure strategy Bayesian Nash equilibrium of this game.
- し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?Consider the following three-Player, extensive-form game - (-2,–1,2) а 2 b 3 Y +(-2,0,0) A (2,0,1) Y 3 (0,0,1) ►(0,0,0) a (0,1,0) (1,1,1) a) Find all pure strategy Nash equilibria of this game. b) Find all pure strategy SPNE of this game.5. Consider the following Extended Form game where P1 stands for Player one and P2 stands for player two with A, B and A', B' being their respective strategies. A' (1,1) P2 B' (2,3) P1 A' B (4,5) P2 What is the set of Nash Equilibria? Clearly explain your answer. Full-screen Snip B' (6,7)