Homework Answers
1. Nash equilibrium is the set of strategies, one for each player, such that no player receives incremental benefits by changing his or her strategy, given that the other player's strategy remains constant.
In this game, the Nash equilibrium is Alice chooses Down and Bob chooses Right.
Answer: option 3
2. If Alice chooses Up, Bob will get 4 by choosing left and 3 by choosing right. As 4 > 3, therefore Bob's best response is to choose left if Alice were to choose Up.
Answer: Bob should choose left.
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Consider the following game table: Bob Left Right Upl Alice Down 3 In this game, is...
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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...
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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 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...
2. consider the following simultaneous move game. Player B LEFT RIGHT Player A UP 4,1 1,4...
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5. [Subgame perfection] Consider the following game. Two friends, Anne (A) and Bob (B), are trying...
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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...
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NEED HELP WITH DISCRETE MATH:
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Consider the following game. Alice and Bob have a an infinite quarter chessboard in front of them. The chessboard has a left edge and a bottom edge. There is one checker on some square the chessboard. The player whose turn it is can move the checker down any positive number of squares, or can move the check one column to the left, but anywhere in that column. The game ends when a player cannot...
Will Up Left Centre Right 2,8 0,9 4,3 3,7 -2,10 2,15 John Down Problem 2 Consider...
Will Up Left Centre Right 2,8 0,9 4,3 3,7 -2,10 2,15 John Down Problem 2 Consider the following simultaneous game given above. 1. What is the set of strategies for each player? 2. Define dominant strategy. Is there a dominant strategy for John? Is there a dominant strategy for Will? Find all dominant strategy equilibria in this game. 3. Define Nash equilibrium. Find all Nash equilibria in this game. 4. Are dominant strategy equilibria always Nash equilibria? Are Nash equilibria...
29. Consider the following game. You and your friend, Alice, are driving cars towards each other....
29. Consider the following game. You and your friend, Alice, are driving cars towards each other. Each of you can either swerve (S), to avoid colliding into the other person, or not swerve (NS). If you both choose NS, then you crash into each other and die. If you both choose S, then the game is a tie. If one person chooses S, and the other chooses NS, then the one who chooses NS wins. The following payoff matrix depicts...
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...
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 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...
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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...
NEED HELP WITH DISCRETE MATH:
.
Consider the following game. Alice and Bob have a an infinite quarter chessboard in front of them. The chessboard has a left edge and a bottom edge. There is one checker on some square the chessboard. The player whose turn it is can move the checker down any positive number of squares, or can move the check one column to the left, but anywhere in that column. The game ends when a player cannot...
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