Consider a subtraction game.![4. [21 pts] Consider a subtraction game with subtraction set S = {1,4} starting with 6 chips. Player I goes first, and if Pla](http://img.homeworklib.com/questions/796d5190-be39-11ea-9e6c-79bf1543eb8d.png?x-oss-process=image/resize,w_560)
Please show the steps and there are a and b question
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Consider a subtraction game.
Please show the steps and there are a and b question
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A subtraction game Subtraction games are two-player games in which there is a pile of objects,...
A subtraction game Subtraction games are two-player games in which there is a pile of objects, say coins. There are two players, Alice and Bob, who alternate turns subtracting 4.9. A SUBTRACTION GAME 19 from the pile some number of coins belonging to a set S (the subtraction set). Alice goes first. The first player who is unable to make a legal move loses. For example, suppose the initial pile contains 5 coins, and each player can, on his turn,...
1. (60 marks) Consider a two-person game, in which every player has two pure strategies to...
1. (60 marks) Consider a two-person game, in which every player has two pure strategies to play. The payoff matrix of the game is as follows Strategy 2 Player One Player Two Strategy I Strategy II Strategy 1 0,0 1,3 1,1 Find all the Nash equilibria of the game.
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...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of player 2's strategies. (2 points) (ii) Construct a payoff matrix and identify all Nash equilibria to the game. (2 points) (iii) Use backwards induction to find all subgame perfect equilibria of the game. (2 points)
Please show ALL STEPS, NEAT HANDWRITNG ONLY and answer ALL PARTS please :) 1. Consider the...
Please show ALL STEPS, NEAT HANDWRITNG ONLY and answer ALL PARTS please :) 1. Consider the following game: suppose there are three piles of stones starting with 3, 5, and 7 in each pile. Two players take turn playing this game. During their turn, a player can choose one of the three piles that are currently nonempty and remove any positive number of stonescurrently presented in that pile. Whoever takes the last stone loses the game. (a) Describe how to...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
3. Consider the game illustrated by the payoff matrix below: Jeffrey B1 B2 -4,- 4 1...
3. Consider the game illustrated by the payoff matrix below: Jeffrey B1 B2 -4,- 4 1 ,-6 Curtis A2 -6,1 0,0 b. Suppose that the game is repeated 10 times and assume a discount factor 8 (where 0< 8 < 1). i. [2] What does each player choose to do in the 10th round of play? ii. [2] Can Curtis and Jeffrey credibly commit to playing (A2, B2) in any of the rounds that they play? c. Suppose now that...
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 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...
Question 3 Consider the game in figure 3. Player 2 LR 3,3 1,4 Player 1 4,1...
Question 3 Consider the game in figure 3. Player 2 LR 3,3 1,4 Player 1 4,1 2,2 Figure 3: A Prisoner's Dilemma game. Assume that the payoffs in the figure are $ values. (i) Assume that both players have risk neutral utility functions. Find all of the Nash equilibria of this game. (ii) Next, assume that the row player has other regarding preferences with a = 0 and B = 3 (while the column player has the same preferences as...
1. (60 marks) Consider a two-person game, in which every player has two pure strategies to play. The payoff matrix of the game is as follows Strategy 2 Player One Player Two Strategy I Strategy II Strategy 1 0,0 1,3 1,1 Find all the Nash equilibria of the game.
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...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of player 2's strategies. (2 points) (ii) Construct a payoff matrix and identify all Nash equilibria to the game. (2 points) (iii) Use backwards induction to find all subgame perfect equilibria of the game. (2 points)
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
3. Consider the game illustrated by the payoff matrix below: Jeffrey B1 B2 -4,- 4 1 ,-6 Curtis A2 -6,1 0,0 b. Suppose that the game is repeated 10 times and assume a discount factor 8 (where 0< 8 < 1). i. [2] What does each player choose to do in the 10th round of play? ii. [2] Can Curtis and Jeffrey credibly commit to playing (A2, B2) in any of the rounds that they play? c. Suppose now that...
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...
Question 3 Consider the game in figure 3. Player 2 LR 3,3 1,4 Player 1 4,1 2,2 Figure 3: A Prisoner's Dilemma game. Assume that the payoffs in the figure are $ values. (i) Assume that both players have risk neutral utility functions. Find all of the Nash equilibria of this game. (ii) Next, assume that the row player has other regarding preferences with a = 0 and B = 3 (while the column player has the same preferences as...
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