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led Notes Problem.4: Strategies and Subgames (4 pts) Consider the following game tree: The payoffs in...
Technology Adoption: During the adoption of a new technology a CEO (player 1) can design a...
Technology Adoption: During the adoption of a new technology a CEO (player 1) can design a new task for a division manager. The new task can be either high level (H) or low level (L). The manager simultaneously chooses to invest in good training (G) or bad training (B). The payoffs from this interaction are given by the following matrix: Player 2 GB 5,4 -5,2 H Player 1 L 2, -2 0,0 a. Present the game in extensive form (a...
Problem 1. (20 points) Consider a game with two players, Alice and Bob. Alice can choose...
Problem 1. (20 points) Consider a game with two players, Alice and Bob. Alice can choose A or B. The game ends if she chooses A while it continues to Bob if she chooses B. Bob then can choose C or D. If he chooses C the game ends, and if he chooses D the game continues to Alice. Finally, Alice can choose E or F and the game ends after each of these choices. a. Present this game as...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe the decisions made in period 1 before they play again in period 2. The final payoffs to each player are the sum of the payoffs obtained in each period. 112 L R T 1,1 5,0 B 0,3 7,7 (a) Represent this game in extensive form (tree diagram. How many subgames are there? (b) Using backward induction, find all subgame perfect Nash equilibria (SPE) in...
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....
Question 1 o, 0 0 21 2 0 0 Consider the extensive form game portrayed above....
Question 1 o, 0 0 21 2 0 0 Consider the extensive form game portrayed above. The top number at a terminal node is player 1's payoff, the middle number is player 2's payoff and the bottom number is player 3's payof. a. Derive the strategy set for each player. (Note: If you do not want to list all of the strategies, you can provide a general description of a player's strategy, give an example, and state how many strategies...
Consider a variant of the Nim game called "Stones". Suppose that initially there is a single...
Consider a variant of the Nim game called "Stones". Suppose that initially there is a single pile of 5 stones and two players, I and II. Each player takes turns picking up either 1 or 2 stones from the pile. Player I moves first, then Player II, then Player I, etc. until all stones have been picked up 3. Assuming that the loser is the player who picks up the last stone, write the game of Stones out in extensive...
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...
Problem : Signaling Games (12 pts) Consider the game of imperfect information depicted in the game...
Problem : Signaling Games (12 pts) Consider the game of imperfect information depicted in the game tree below: BE Cowboy is coward Cowboy is Gunslinger Prob. - Quiche Quiche In this game, the players are a Cowboy who wanders into a town in the Wild West, and an Outlaw who terrorizes the town. The Cowboy may be either a Coward or a Gunslinger: the probability p of each state is 0.5. The Cowboy knows which type they are but the...
Identify the definition for each term from the following list. 1. Payoff-matrix format 2. Game-tree format...
Identify the definition for each term from the following list. 1. Payoff-matrix format 2. Game-tree format 3. A junction on a game tree. 4. One of the final outcomes of a game tree. 5. Divides the overall game tree into nested subgames before working backward from right to left. 6. A mini-game within the overall game. 7. The process of backward induction that relies on both firms having perfect information about the decisions made in each subgame. 8. A statement...
07. Consider the following game table: COLIN Left Center Right Top 4 3,5 ,2 2 3,1...
07. Consider the following game table: COLIN Left Center Right Top 4 3,5 ,2 2 3,1 2,3 ROWENA Middle Bottom ---,3 3,4 4,2 130 [CH. 4) SIMULTANEOUS-MOVE GAMES: DISCRETE STRATEGIES (a) Complete the payoffs of the game table above so that Colin has a dominant strategy. State which strategy is dominant and explain why. (Note: There are many equally correct answers.) (b) Complete the payoffs of the game table above so that neither player has a dominant strategy, but also...
Technology Adoption: During the adoption of a new technology a CEO (player 1) can design a new task for a division manager. The new task can be either high level (H) or low level (L). The manager simultaneously chooses to invest in good training (G) or bad training (B). The payoffs from this interaction are given by the following matrix: Player 2 GB 5,4 -5,2 H Player 1 L 2, -2 0,0 a. Present the game in extensive form (a...
Problem 1. (20 points) Consider a game with two players, Alice and Bob. Alice can choose A or B. The game ends if she chooses A while it continues to Bob if she chooses B. Bob then can choose C or D. If he chooses C the game ends, and if he chooses D the game continues to Alice. Finally, Alice can choose E or F and the game ends after each of these choices. a. Present this game as...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe the decisions made in period 1 before they play again in period 2. The final payoffs to each player are the sum of the payoffs obtained in each period. 112 L R T 1,1 5,0 B 0,3 7,7 (a) Represent this game in extensive form (tree diagram. How many subgames are there? (b) Using backward induction, find all subgame perfect Nash equilibria (SPE) in...
Question 1 o, 0 0 21 2 0 0 Consider the extensive form game portrayed above. The top number at a terminal node is player 1's payoff, the middle number is player 2's payoff and the bottom number is player 3's payof. a. Derive the strategy set for each player. (Note: If you do not want to list all of the strategies, you can provide a general description of a player's strategy, give an example, and state how many strategies...
Consider a variant of the Nim game called "Stones". Suppose that initially there is a single pile of 5 stones and two players, I and II. Each player takes turns picking up either 1 or 2 stones from the pile. Player I moves first, then Player II, then Player I, etc. until all stones have been picked up 3. Assuming that the loser is the player who picks up the last stone, write the game of Stones out in extensive...
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...
Problem : Signaling Games (12 pts) Consider the game of imperfect information depicted in the game tree below: BE Cowboy is coward Cowboy is Gunslinger Prob. - Quiche Quiche In this game, the players are a Cowboy who wanders into a town in the Wild West, and an Outlaw who terrorizes the town. The Cowboy may be either a Coward or a Gunslinger: the probability p of each state is 0.5. The Cowboy knows which type they are but the...
Identify the definition for each term from the following list. 1. Payoff-matrix format 2. Game-tree format 3. A junction on a game tree. 4. One of the final outcomes of a game tree. 5. Divides the overall game tree into nested subgames before working backward from right to left. 6. A mini-game within the overall game. 7. The process of backward induction that relies on both firms having perfect information about the decisions made in each subgame. 8. A statement...
07. Consider the following game table: COLIN Left Center Right Top 4 3,5 ,2 2 3,1 2,3 ROWENA Middle Bottom ---,3 3,4 4,2 130 [CH. 4) SIMULTANEOUS-MOVE GAMES: DISCRETE STRATEGIES (a) Complete the payoffs of the game table above so that Colin has a dominant strategy. State which strategy is dominant and explain why. (Note: There are many equally correct answers.) (b) Complete the payoffs of the game table above so that neither player has a dominant strategy, but also...
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