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Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills...
Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills...
Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills and can take one of the following two actions: (i) she can give S20 to Bob or (ii) she can give one of the S10 bills to Bob. All the money will be used to buy popcorns before the movie they will see. Each one dollar of popcorn gives one unit of payoff for the player who buys it. In the second step, they...
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...
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...
GAME MATRIX Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
Problem 3 - Battle of the sexes with a first mover Consider once again Tony and...
Problem 3 - Battle of the sexes with a first mover Consider once again Tony and Maria and their movie night coordination game. Tony and Maria have different preferences for movies. Tony prefers Action movies over Comedies. Maria prefers Comedies to Action movies. They prefer to watch movies together rather than separately. The payoff matrix is as follows. Table 1: Tony and Maria payoffs Tony Action Comedy Action 2,5 -1,-1 Maria Comedy 1.1 5,2 1. Determine all the pure strategy...
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...
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...
4) (20 points) Consider the following two player simultaneous move game which is another version of...
4) (20 points) Consider the following two player simultaneous move game which is another version of the Battle of the Sexes game. Bob Opera Alice 4,1 Opera Football Football 0,0 1,4 0,0 Suppose Alice plays a p - mix in which she plays Opera with probability p and Football with probability (1 – p) and Bob plays a q- mix in which he plays Opera with probability q and Football with probability (1 – 9). a) Find the mixed strategy...
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...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills and can take one of the following two actions: (i) she can give S20 to Bob or (ii) she can give one of the S10 bills to Bob. All the money will be used to buy popcorns before the movie they will see. Each one dollar of popcorn gives one unit of payoff for the player who buys it. In the second step, they...
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...
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...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
Problem 3 - Battle of the sexes with a first mover Consider once again Tony and Maria and their movie night coordination game. Tony and Maria have different preferences for movies. Tony prefers Action movies over Comedies. Maria prefers Comedies to Action movies. They prefer to watch movies together rather than separately. The payoff matrix is as follows. Table 1: Tony and Maria payoffs Tony Action Comedy Action 2,5 -1,-1 Maria Comedy 1.1 5,2 1. Determine all the pure strategy...
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...
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...
4) (20 points) Consider the following two player simultaneous move game which is another version of the Battle of the Sexes game. Bob Opera Alice 4,1 Opera Football Football 0,0 1,4 0,0 Suppose Alice plays a p - mix in which she plays Opera with probability p and Football with probability (1 – p) and Bob plays a q- mix in which he plays Opera with probability q and Football with probability (1 – 9). a) Find the mixed strategy...
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...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
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