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5. Consider the payoff matrix below, which shows two players each with three strategies. Player 2...
1. Find the Nash equilibria of the two-player strategic game in which each players set of...
1. Find the Nash equilibria of the two-player strategic game in which each players set of actions (strategies) is the set of nonnegative numbers and the players payoff functions are ui(a1, a2)- a1 (a2-a1) and u2 (a1, a2) = a2 (1-al-a2).
GAME 3 Player B B1 B2 Player A A1 7,3 5, 10 A2 3,8 9,6 In...
GAME 3 Player B B1 B2 Player A A1 7,3 5, 10 A2 3,8 9,6 In Game 3 above, if the players move sequentially with Player B choosing first, the Nash equilibrium will be a) Player A choosing A2 and Player B choosing B1 b) Player A choosing A2 and Player B choosing B2 c) Player A choosing A1 and Player B choosing B2 d) Player A choosing A1 and Player B choosing B1
Player B Move B Mone B -1.-2 1.-3 2,3 2,2 The payoff matrix shows Player A...
Player B Move B Mone B -1.-2 1.-3 2,3 2,2 The payoff matrix shows Player A Movedi Move A Player A having two moves (A) and A) and Player B having two moves (B, and B). In each cell, Player A's payoff is on the left and Player B's payoff is on the right. What is the dominant strategy for each player assuming that they play/choose simultaneously. Select one: O a. Dominant strategies are A, B. O b. Dominant strategies...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are up and down, and player 2's strategies are left and right. Suppose that player 1's payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0. Suppose further that player 2's payoff function is such that no two combinations of the players' chosen strategies ever give player 2 the same payoff Choose the...
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...
3. Consider the game illustrated by the payoff matrix below: Jeffrey B1 B2 -4,- 4 1...
3. Consider the game illustrated by the payoff matrix below: Jeffrey B1 B2 -4,- 4 1 ,-6 Curtis A2 -6,1 0,0 b. Suppose that the game is repeated 10 times and assume a discount factor 8 (where 0< 8 < 1). i. [2] What does each player choose to do in the 10th round of play? ii. [2] Can Curtis and Jeffrey credibly commit to playing (A2, B2) in any of the rounds that they play? c. Suppose now that...
GAME MATRIX Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
11. The demand for a monopolist's product is given by Q - 400 4P while the...
11. The demand for a monopolist's product is given by Q - 400 4P while the monopolist's marginal cost is given by MC-2Q The profit-maximizing quantity of output for this monopolist is A) 100 C) 40 B) 44-44 D) 20 There is a payoff matrix of two firms; their different profits are listed when they choose collusion or competition (answer 14-15). firm B collusion 27.5 19, 19 competition competition14, 14 5. 28 firm A collusion 12. In the game above,...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1 moves twice: Player 1 chooses Enter or Erit, and if she chooses Exit the game ends with payoffs of 2 to player 2 and 0 to player 1. • Player 2 observes player l's choice and will have a choice between Fight or Help if player 1 chose Enter. Choosing Help ends the game with payoffs of 1 to both players. • Finally, player...
Consider the following two player game. The players’ strategy spaces are SA = {a1, a2, a3}...
Consider the following two player game. The players’ strategy
spaces are SA = {a1, a2, a3} and SB = {b1, b2, b3, b4}.
(d) Derive all the rationalizable strategy profiles.
(e) Derive the players’ best reply correspondences.
(f) Compute all the Nash equilibria of the game
A\В by 2, 2 3, 1 8,0 3, 6 а1 3, 1 0, 6 1, 4 1, 0 а2 4, 2 1, 1 2, 2 4, 4 аз
A\В by 2, 2 3, 1...
1. Find the Nash equilibria of the two-player strategic game in which each players set of actions (strategies) is the set of nonnegative numbers and the players payoff functions are ui(a1, a2)- a1 (a2-a1) and u2 (a1, a2) = a2 (1-al-a2).
GAME 3 Player B B1 B2 Player A A1 7,3 5, 10 A2 3,8 9,6 In Game 3 above, if the players move sequentially with Player B choosing first, the Nash equilibrium will be a) Player A choosing A2 and Player B choosing B1 b) Player A choosing A2 and Player B choosing B2 c) Player A choosing A1 and Player B choosing B2 d) Player A choosing A1 and Player B choosing B1
Player B Move B Mone B -1.-2 1.-3 2,3 2,2 The payoff matrix shows Player A Movedi Move A Player A having two moves (A) and A) and Player B having two moves (B, and B). In each cell, Player A's payoff is on the left and Player B's payoff is on the right. What is the dominant strategy for each player assuming that they play/choose simultaneously. Select one: O a. Dominant strategies are A, B. O b. Dominant strategies...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are up and down, and player 2's strategies are left and right. Suppose that player 1's payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0. Suppose further that player 2's payoff function is such that no two combinations of the players' chosen strategies ever give player 2 the same payoff Choose the...
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...
3. Consider the game illustrated by the payoff matrix below: Jeffrey B1 B2 -4,- 4 1 ,-6 Curtis A2 -6,1 0,0 b. Suppose that the game is repeated 10 times and assume a discount factor 8 (where 0< 8 < 1). i. [2] What does each player choose to do in the 10th round of play? ii. [2] Can Curtis and Jeffrey credibly commit to playing (A2, B2) in any of the rounds that they play? c. Suppose now that...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
11. The demand for a monopolist's product is given by Q - 400 4P while the monopolist's marginal cost is given by MC-2Q The profit-maximizing quantity of output for this monopolist is A) 100 C) 40 B) 44-44 D) 20 There is a payoff matrix of two firms; their different profits are listed when they choose collusion or competition (answer 14-15). firm B collusion 27.5 19, 19 competition competition14, 14 5. 28 firm A collusion 12. In the game above,...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1 moves twice: Player 1 chooses Enter or Erit, and if she chooses Exit the game ends with payoffs of 2 to player 2 and 0 to player 1. • Player 2 observes player l's choice and will have a choice between Fight or Help if player 1 chose Enter. Choosing Help ends the game with payoffs of 1 to both players. • Finally, player...
Consider the following two player game. The players’ strategy
spaces are SA = {a1, a2, a3} and SB = {b1, b2, b3, b4}.
(d) Derive all the rationalizable strategy profiles.
(e) Derive the players’ best reply correspondences.
(f) Compute all the Nash equilibria of the game
A\В by 2, 2 3, 1 8,0 3, 6 а1 3, 1 0, 6 1, 4 1, 0 а2 4, 2 1, 1 2, 2 4, 4 аз
A\В by 2, 2 3, 1...
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