Consider a sequential move game with two players. If the player who moves first has two...
Consider a sequential move game with two players. If the player who moves first has two or more strategies that offer him the same payoff, which one will he choose?
Homework Answers
The player will solve the game using backward induction and find
the one strategy which will be his most profitable strategy using
backward induction Nash.
Another strategy can be choosing the one which gives a lower payoff to the second player.
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Consider a sequential move game with two players. If the player
who moves first has two...
Q1. Suppose two players, First and Second, take part in a sequential-move game. First moves first,...
Q1. Suppose two players, First and Second, take part in a sequential-move game. First moves first, Second moves second, and each player moves only once. (a). Draw a game tree for a game in which First has two possible actions (Up or Down), and Second has three possible actions (Top, Middle, or Bottom) at each node. Show which nodes are terminal/decision and write down all the (pure) strategies of each player. (b). Draw a game tree for a game in...
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...
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...
In a simultaneous move game, both players make their strategy choices at the same time. In...
In a simultaneous move game, both players make their strategy choices at the same time. In a sequential move game, one player chooses his strategy first, and then seeing the move that the first player made, the second player chooses her strategy. Hence, in sequential game player is better informed and will act accordingly, than in simultaneous move game where he faces risk between different strategies.
Consider a game in which Player 1 first selects between L and R. If Player 1...
Consider a game in which Player 1 first selects between L and R. If Player 1 selects L, then players 1 and 2 play a prisoner’s dilemma game represented in the strategic form above. If Player 1 selects R then, Player 1 and 2 play the battle-of-the-sexes game in which they simultaneously and independently choose between A and B. If they both choose A, then the payoff vector is (4,4). If they both choose B, then the payoff vector is...
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...
(a) There are two players in this game - A and B. A moves first and can go either left L or right...
(a) There are two players in this game - A and B. A moves first and can go either left L or right R. B does not see what A did, and can go either up U or down D. If B went D, A moves again, and can choose 1, c, or r. If B went U then A can move again only if he started with going L in the beginning. In this case A can choose either...
Brothers: Consider the following game that proceeds in two stages: In the first stage one brother...
Brothers: Consider the following game that proceeds in two stages: In the first stage one brother (player 2) has two $10 bills and can choose one of two options: he can give his younger brother (player 1) $20 or give him one of the $10 bills (giving nothing is inconceivable given the way they were raised). This money will then be used to buy snacks at the show they will see, and each $1 of snacks purchased yields one unit...
4. Consider the following game that is played T times. First, players move simultaneously and independently....
4. Consider the following game that is played T times. First, players move simultaneously and independently. Then each player is informed about the actions taken by the other player in the first play and, given this, they play it again, and so on. The payoff for the whole game is the sum of the payoffs a player obtains in the T plays of the game A 3,1 4,0 0,1 В 1,5 2,2 0,1 C 1,1 0,2 1,2 (a) (10%) Suppose...
6. Consider a sequential game with 3 players. Player 1 can choose A or B. Player...
6. Consider a sequential game with 3 players. Player 1 can choose A or B. Player 2 can choose C, D, E, or F (depending on what player 1 chooses). Player 3 can choose G, H, I, J, K, L, M, or N (depending on what player 1 and 2 choose). Player 1 (P1) goes first, player 2 (P2) goes second, and player 3 (P3) goes third. Payoffs are written as the payoffs for P1, P2, and the for P3....
Q1. Suppose two players, First and Second, take part in a sequential-move game. First moves first, Second moves second, and each player moves only once. (a). Draw a game tree for a game in which First has two possible actions (Up or Down), and Second has three possible actions (Top, Middle, or Bottom) at each node. Show which nodes are terminal/decision and write down all the (pure) strategies of each player. (b). Draw a game tree for a game in...
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...
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...
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...
(a) There are two players in this game - A and B. A moves first and can go either left L or right R. B does not see what A did, and can go either up U or down D. If B went D, A moves again, and can choose 1, c, or r. If B went U then A can move again only if he started with going L in the beginning. In this case A can choose either...
Brothers: Consider the following game that proceeds in two stages: In the first stage one brother (player 2) has two $10 bills and can choose one of two options: he can give his younger brother (player 1) $20 or give him one of the $10 bills (giving nothing is inconceivable given the way they were raised). This money will then be used to buy snacks at the show they will see, and each $1 of snacks purchased yields one unit...
4. Consider the following game that is played T times. First, players move simultaneously and independently. Then each player is informed about the actions taken by the other player in the first play and, given this, they play it again, and so on. The payoff for the whole game is the sum of the payoffs a player obtains in the T plays of the game A 3,1 4,0 0,1 В 1,5 2,2 0,1 C 1,1 0,2 1,2 (a) (10%) Suppose...
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