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3. (15 points) Consider a sequential game with two players with three-moves, in which player 1...
In the extensive form representation of the game between Player 1 and Player 2, Player 1...
In the extensive form representation of the game between Player 1 and Player 2, Player 1 moves first and chooses L or R. If Player 1 chooses R the game ends, if Player 1 chooses L then Player 1 and 2 play a simultaneous move game. The game has______________ pure strategy Nash equilibria and__________ pure strategy Subgame Perfect Nash Equilibria (SPNE). The maximum payoff Player 2 gets in a SPNE is___________ . (Please, enter only numerical answers like: 1, 2,...
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. 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....
2) Here's another game: There are three players, numbered 1,2, and 3. At the beginning of...
2) Here's another game: There are three players, numbered 1,2, and 3. At the beginning of the game, players1 and 2 simultaneously make decisions, each pulling out a Red or Blue marble. Neither player can see what the other player is choosing. After this choice, the players secretly reveal their marbles to each other without letting player 3 see. If both players choose Red, then the game ends and the payoff vector is(, 0, 0). If both players choose Blue,...
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 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?
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...
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...
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...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2....
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
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...
2) Here's another game: There are three players, numbered 1,2, and 3. At the beginning of the game, players1 and 2 simultaneously make decisions, each pulling out a Red or Blue marble. Neither player can see what the other player is choosing. After this choice, the players secretly reveal their marbles to each other without letting player 3 see. If both players choose Red, then the game ends and the payoff vector is(, 0, 0). If both players choose Blue,...
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...
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...
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...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
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