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Consider the sequential game depicted in the figure below. Player A moves first. She can charge...
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...
Nsider the Game of Chicken depicted in the figure below, in which t each other must decide whethe...
need d, e and f answered. first picture is just for reference to
the questions.
nsider the Game of Chicken depicted in the figure below, in which t each other must decide whether or not to swerve. Player 2 Straight Swerve Player 1 Straight 0, 0 Swerve1,3 3, 1 2, 2 have a strictly dominant strategy? What about Player 2? best responses for Player 1? And for Player 2? any pure strategy Nash Equilibrium (psNE) in this game? d. Find...
Consider the competitive, static, one-time game depicted in the following figure. If larger payoffs are preferred,...
Consider the competitive, static, one-time game depicted in the following figure. If larger payoffs are preferred, does either player have a dominant strategy? If B believes that A will move A1, how should B move? If B believes that A will move A2, how should B move? What is the Nash equilibrium strategy profile if this game is played just once? What is the strategy profile for this game if both players adopt a secure strategy? What strategy profile results...
Homework #1 Consider a 3-player setting in which player 1 moves first by choosing among three...
Homework #1 Consider a 3-player setting in which player 1 moves first by choosing among three actions: a, b, and c. After observing the choice of player 1, player 2 chooses among two actions: x and y. 1. Consider the following three variants as to what player 3 can do and what she knows when she moves: If player 1 chose a, then (after player 2 made his choice) player 3 selects among two actions: high and low. Player 3...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
Consider an investment game among 2 players. Each player can either invest, i, or not invest,-i....
Consider an investment game among 2 players. Each player can either invest, i, or not invest,-i. If a player does not invest, her payoff is 0 regardless of whether the other invests or not. If a player invests, she gets 1 if the other invests but -1 if at least one of the others does not. a. What are the pure Nash equilibria? b. What is the Pareto dominant pure Nash equilibrium? c. What is the Risk dominant pure Nash...
You play the following bargaining game. Player A moves first and makes Player B an offer...
You play the following bargaining game. Player A moves first and makes Player B an offer for the division of $1000. (For example, Player A could suggest that she take $600 and Player B take $400.) Player B can accept or reject the offer. If he rejects it, the amount of money available drops to $900, and he then makes an offer for the division of this amount. If Player A rejects this offer, the amount of money drops...
Consider the following game: there are two players, an incumbent (denoted I) and a potential entrant...
Consider the following game: there are two players, an incumbent (denoted I) and a potential entrant (denoted E) to the market. The entrant has two actions: it can either enter the market in which the incumbent operates, or not enter. The incumbent has two actions: it can either fight the entrant, or accommodate. The payoffs are as follows: if E enters and I fights, E gets -1 and I gets 2. If E does not enter, I gets 10 for...
Consider a game in which, simultaneously, player 1 selects a number x and player 2 select...
Consider a game in which, simultaneously, player 1 selects a number x and player 2 select a number y, where x and y must be greater than or equal to 0. Player 1's payoff is U1 = 8x - 2xy - x2 and player 2's payoff is U2 = 4by + 2xy - y? The parameter b is privately known to player 2. Player 1 knows only that b = O with probability 1/2 and b = 4 with probability...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2....
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
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...
need d, e and f answered. first picture is just for reference to
the questions.
nsider the Game of Chicken depicted in the figure below, in which t each other must decide whether or not to swerve. Player 2 Straight Swerve Player 1 Straight 0, 0 Swerve1,3 3, 1 2, 2 have a strictly dominant strategy? What about Player 2? best responses for Player 1? And for Player 2? any pure strategy Nash Equilibrium (psNE) in this game? d. Find...
Homework #1 Consider a 3-player setting in which player 1 moves first by choosing among three actions: a, b, and c. After observing the choice of player 1, player 2 chooses among two actions: x and y. 1. Consider the following three variants as to what player 3 can do and what she knows when she moves: If player 1 chose a, then (after player 2 made his choice) player 3 selects among two actions: high and low. Player 3...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
Consider a game in which, simultaneously, player 1 selects a number x and player 2 select a number y, where x and y must be greater than or equal to 0. Player 1's payoff is U1 = 8x - 2xy - x2 and player 2's payoff is U2 = 4by + 2xy - y? The parameter b is privately known to player 2. Player 1 knows only that b = O with probability 1/2 and b = 4 with probability...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
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