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IV. Consider the following game tree and the given choice functions for players P, Pa, and...
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0)...
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0) (-1,0) (-1,1) C (0,1) (1,0) (0,2) (0,2) (0,2) A В (0,2) 1,2) (0,2) (0,2) (0,3) (0,4) (-1,3) (0,3) a. Use the Elimination of Weakly Dominated Strategies Criterion to obtain a solution (unique to the chosen order of elimination) b. Show that the order of elimination matters by finding a different solution (unique to the new chosen order of elimination) c. Show that the solutions...
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....
1. Consider a market for mid-size sedan with two players, Toyota and Kia. Each company can...
1. Consider a market for mid-size sedan with two players, Toyota and Kia. Each company can set either high price (say $30,000) or low price (say $25,000) for their signature mid-size sedan model. The summary of the game is provided by a 2x2 matrix below. The first number in each payoff box is for Kia and the second number is for Toyota. Toyota Low P High P Kia Low P 0,0 2,-1 High P -1,2 1,1 (a) Identify the Nash...
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...
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...
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 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...
Problems 3,4 and 5 Problem 3. Consider the game below. (a) There are no dominant or...
Problems 3,4 and 5
Problem 3. Consider the game below. (a) There are no dominant or dominated strategies. Is there anything you can say about what players will do? Player 2 C T (2,1) (0,2) M (1,1) (1,1)| (1,0) B(0,1) (2,0) (2,2) (0,3) Player (b) Report the best responses Problem 4. Bertrand Competition With Different Costs Suppose two firms facing a demand Dip) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost e and Firm...
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...
1. Consider the coupon game. But suppose that instead of decisions being made simultaneously, they are made sequentially, with Firm 1 choosing first, and its choice observed by Firm 2 before Firm 2 ma...
1. Consider the coupon game. But suppose that instead of
decisions being made simultaneously, they are made sequentially,
with Firm 1 choosing first, and its choice observed by Firm 2
before Firm 2 makes its choice.
a. Draw a game tree representing this game.
b. Use backward induction to find the solution. (Remember that
your solution should include both firms’ strategies, and that Firm
2’s strategy should be complete!)
2. Two duopolists produce a homogeneous product, and each has a...
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0) (-1,0) (-1,1) C (0,1) (1,0) (0,2) (0,2) (0,2) A В (0,2) 1,2) (0,2) (0,2) (0,3) (0,4) (-1,3) (0,3) a. Use the Elimination of Weakly Dominated Strategies Criterion to obtain a solution (unique to the chosen order of elimination) b. Show that the order of elimination matters by finding a different solution (unique to the new chosen order of elimination) c. Show that the solutions...
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...
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...
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 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...
Problems 3,4 and 5
Problem 3. Consider the game below. (a) There are no dominant or dominated strategies. Is there anything you can say about what players will do? Player 2 C T (2,1) (0,2) M (1,1) (1,1)| (1,0) B(0,1) (2,0) (2,2) (0,3) Player (b) Report the best responses Problem 4. Bertrand Competition With Different Costs Suppose two firms facing a demand Dip) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost e and Firm...
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...
1. Consider the coupon game. But suppose that instead of
decisions being made simultaneously, they are made sequentially,
with Firm 1 choosing first, and its choice observed by Firm 2
before Firm 2 makes its choice.
a. Draw a game tree representing this game.
b. Use backward induction to find the solution. (Remember that
your solution should include both firms’ strategies, and that Firm
2’s strategy should be complete!)
2. Two duopolists produce a homogeneous product, and each has a...
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