Homework Answers
- If player 1 chooses U, then the best response of player 2 is to choose L
- If player 1 chooses D, then the best response of player 2 is to choose L
Similarly,
- if player 2 chooses L, then the best response of player 1 is to choose U
- if player 2 chooses R, then the best response of player 1 is to choose D
Hence, the Nash Equilibrium (U, L)
Player 1 chooses U and Player 2 chooses L
Option 3rd is correct
**if you liked the answer, then please upvote. Would be motivating for me. Thanks.
1 pts Question 8 U Player 2 L R U 2.0 2,1 Player 1 D 3,1...
1 pts Question 8 U Player 2 L R U 2.0 2,1 Player 1 D 3,1 1,2 The above figure shows the payoff matrix for two players, Player 1 and Player 2. Player 1's payoff is listed first in each cell. A Nash equilibrium of this game is that Player 1 chooses and Player 2 chooses L. Player 1 chooses and Player 2 chooses R. Player 1 chooses and Player 2 chooses L. Player 1 chooses U and Player 2...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10...
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10 20.30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The tab...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
3. Player 1 and Player 2 are going to play the following stage game twice: &n...
3. Player 1 and Player 2 are going to play the following stage
game twice:
Player 2
Left
Middle
Right
Player 1
Top
4, 3
0, 0
1, 4
Bottom
0, 0
2, 1
0, 0
There is no discounting in this problem and so a player’s payoff
in this repeated game is the sum of her payoffs in the two plays of
the stage game.
(a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
8. Consider the two-player game described by the payoff matrix below. Player B L R Player...
8. Consider the two-player game described by the payoff matrix below. Player B L R Player A D 0,0 4,4 (a) Find all pure-strategy Nash equilibria for this game. (b) This game also has a mixed-strategy Nash equilibrium; find the probabilities the players use in this equilibrium, together with an explanation for your answer (c) Keeping in mind Schelling's focal point idea from Chapter 6, what equilibrium do you think is the best prediction of how the game will be...
The following matrix gives the payoff for Player 1 and Player 2 with R and L...
The following matrix gives the payoff for Player 1 and Player 2 with R and L strategies. Assume that they determine their strategies simultaneously and independently. Player 2 R L R (5, 4) (-1, -1) Player 1 L (-1, -1) (2, 2) (a) Does Player 1 have a dominant strategy? Why or why not? What is its dominant strategy, if existing? (b) Does Player 2 have a dominant strategy? Why or why not? What is its dominant strategy, if existing?...
Check my work In a two-player, one-shot simultaneous-move game each player can choose strategy A or...
Check my work In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy Band player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. payoff...
Player lI A 6,6 2,0 В 0,1 а,а Player Consider the game represented above in which...
Player lI A 6,6 2,0 В 0,1 а,а Player Consider the game represented above in which BOTH Player 1 and Player 2 get a payoff of "a" when the strategy profile played is (B,D). Select the correct answer. If a-1 then strategy B is strictly dominated If a-3/2 then the game has two pure strategy Nash Equilibria. For all values of "a" strategy A is strictly dominant. For small enough values of "a", the profile (A,D) is a pure strategy...
Consider a game between a police officer (player 3) and two drivers (players 1 and 2)....
Consider a game between a police officer (player 3) and two drivers (players 1 and 2). Player 1 lives and drives in Wynwood, whereas player 2 lives and drives in Sweetwater. On a given day, players 1 and 2 each have to decide whether or not to use their cell phones while driving. They are not friends, so they will not be calling each other. Thus, whether player 1 uses a cell phone is independent of whether player 2 uses...
1 pts Question 8 U Player 2 L R U 2.0 2,1 Player 1 D 3,1 1,2 The above figure shows the payoff matrix for two players, Player 1 and Player 2. Player 1's payoff is listed first in each cell. A Nash equilibrium of this game is that Player 1 chooses and Player 2 chooses L. Player 1 chooses and Player 2 chooses R. Player 1 chooses and Player 2 chooses L. Player 1 chooses U and Player 2...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10 20.30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
3. Player 1 and Player 2 are going to play the following stage
game twice:
Player 2
Left
Middle
Right
Player 1
Top
4, 3
0, 0
1, 4
Bottom
0, 0
2, 1
0, 0
There is no discounting in this problem and so a player’s payoff
in this repeated game is the sum of her payoffs in the two plays of
the stage game.
(a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
8. Consider the two-player game described by the payoff matrix below. Player B L R Player A D 0,0 4,4 (a) Find all pure-strategy Nash equilibria for this game. (b) This game also has a mixed-strategy Nash equilibrium; find the probabilities the players use in this equilibrium, together with an explanation for your answer (c) Keeping in mind Schelling's focal point idea from Chapter 6, what equilibrium do you think is the best prediction of how the game will be...
Check my work In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy Band player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. payoff...
Player lI A 6,6 2,0 В 0,1 а,а Player Consider the game represented above in which BOTH Player 1 and Player 2 get a payoff of "a" when the strategy profile played is (B,D). Select the correct answer. If a-1 then strategy B is strictly dominated If a-3/2 then the game has two pure strategy Nash Equilibria. For all values of "a" strategy A is strictly dominant. For small enough values of "a", the profile (A,D) is a pure strategy...
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