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- In trying to solve for the Cournot - Nash equilibrium, given (",") = R₁ (2) = 60-2 60-2 and (v) = R₂₁ = solve for y, . Answer: 45-1 2 C In trying to solve for the Cournot-Nash equilibrium, given (y) R₁(y)=60-y and = (y) R₂(y)= 45-y solve for y 2 Answer:Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.Problem #4: Bayesian Nash Equilibrium Consider the following game, which has two states of nature shown in the two game tables below: "Harmful" (p = 1/3) "Helpful" (1-p = 2/3) Player 2 X Y 3, 2 Player 2 Y 2, 3 3, 2 1,0 0,1 A 0,1 3,2 A Player 1 Player 1 В 0,1 B a) Assume that Player 1 knows what the true state of nature is when playing this game, but Player 2 does not. Find all of the game's Bayesian Nash equilibria. (Hint: It may help to arrange the game tables appropriately.) b) Now, assume that Player 2 knows the true state of nature, but Player 1 does not. Find all of the game's Bayesian Nash equilibria.
- Suppose there is a game between two players where each can choose either 'A' or 'B'. If the strategy 'B' is strictly dominant for Player 1 and the strategy 'A' is strictly dominant for Player 2 then which of the following is true? There could be an interior mixed strategy Nash equilibrium There could be multiple pure strategy Nash equilibria There is no Nash equilibrium There is a Nash equilibrium at (B,A) More than one of the aboveConsider two players in the game-theoretic setting below: Player 2 Choice A Choice B Choice 20 |-30 A -20 30 Player 1 Choice |-30 40 B 30 -40 What is the (pure-strategy) Nash equilibrium? There are more than one (pure-strategy) Nash equilibria. O (P1, P2) = (A, B) is the only (pure-strategy) Nash equilibrium. O (P1, P2) = (A, A) is the only (pure-strategy) Nash equilibrium. O There is no (pure-strategy) Nash equilibrium. O (P1, P2) = (B, A) is the only (pure-strategy) Nash equilibrium. (P1, P2) = (B, B) is the only (pure-strategy) Nash equilibrium.which is the nash equilibrium? small pig does press large pig does press (20, 130), small pig doesn't press large pig does press (140, 10), small pig does press large pig doesn't press (-5, 150), small pig does not press large pig doesn't press (0,0).
- 6. Battle of the Networks 1\2 %share Sitcom Sitcom 48;52 Sport 42;58 Nature 55:45 58;42 Ans: s; = (0; 0.85; 0.14); V, = 55.43 s; = (0.43; 0.57;0); V½ = 44.57 40;60 63;37 60;40 Sport Nature 56:44 52;48 Find Nash Equilibrium.Consider the Normal Form Game characterized in the following figure: P1 \ P2 A1 A2 A3 A4 B1 B2 B3 B4 (-1,1) (0,0) (1,-1) (2,0) (-2,-2) (2,7) (-1,-1) (-1,1) (5,7) (3,5) (0,0) (0,8) (0,3) (-1,-1) (10,2) (0,0) Which is the set of rationalizable actions? O (A2, A4)x(B2, B3) O (A1, A2)x(B1, B2, B4) O (A1, A3)x(B1, B4) O (A1, A3, A4}x{B1, B3)Find all Nash Equilibria for the following instance of BESTRESPONSEDYNAMICS. 4 6 12 15 3 Y 2 11 4 1 T1 T2 T3
- AsapNash equilibrium refers to the optimal outcome of a game where there is no incentive for the players to deviate from their initial strategy. An individual (or player) can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. Given this premise, can there be a no Nash equilibrium?Player 2 Left P1: $40 Player 1 Up P2: $0 P1: $44 Down P2:$44 In the game shown above, list all of the EFFICIENT Nash Equilibrium (please check ALL that apply) (up, left) (up, right) (down, left) (down, right) No efficient Nash Equilibrium Right P1:$1 P2: $1 P1: $0 P2: $40
