(Game Theory) In the subtraction game where players may subtract 1, 2 or 5 chips on...

(Game Theory) In the subtraction game where players may subtract 1, 2 or 5 chips on their turn, identify the N- and P-positions. (Please do not forget to prove correctness of your answer.)

Expert Solution

Colby Messinger answered 6 months ago

A sequential game with two-players 1 and 2, where player 1 has the first move advantage....

A sequential game with two-players 1 and 2, where player 1 has the first move advantage. Each player has two strategies, A and B. If both players choose A, each gets a payoff of 2. Both choose B, each gets a payoff of 3. For player 1 choose A and player 2 choose B, player 1 gets 4, and player 2 gets 1. If player 1 chooses B and player 2 choose A, player 1 gets a payoff of 1,...

PSEUDOCODE: 1. You are designing a 2 dimensional game where players shoot bullets hugs at each...

PSEUDOCODE: 1. You are designing a 2 dimensional game where players shoot bullets hugs at each other. Define a pseudocode function to determine whether a hug successfully 'hit' a player at a particular moment. Real parameter playerX : target player's x position Real parameter playerY : target player's y position Real parameter bulletX : x position of bullet Real parameter bulletY : y position of bullet Return Boolean : True if distance between target and player within 10 False if...

Coin taking game This game is played between 2 players, player 1 and player 2. There...

Coin taking game This game is played between 2 players, player 1 and player 2. There are two piles of coins. The values of a coin can be any integer. Both players know the values of all coins in both piles. Player 1 makes the first move, and play alternates between the players. A move consists of taking a coin from the top of either of the piles (either player can take from either pile). The game ends when both...

1-If a static game where both players have dominant strategies was to be played sequentially, A....

1-If a static game where both players have dominant strategies was to be played sequentially, A. the outcome of the dynamically played game would be the same with the outcome of the simultaneously played game. B. the Nash equilibrium of the game will not be sub-game perfect. C. the dominant strategies will no longer exist. D. the outcome of the dynamically played game would be different than the outcome of the simultaneously played game. 2- A sub-game perfect Nash equilibrium...

Consider the Stage Game below, and consider the repeated game where players play twice (T =...

Consider the Stage Game below, and consider the repeated game where players play twice (T = 2). Payoﬀs for each agent are simply period one plus period two payoﬀs. L C R T 6,6 0,7 1,2 M 7,0 1,1 2,0 B 2,1 0,1 3,3 (a) Do any strategies dominate any other? (b) What are the two NE of the Stage Game? What is the diﬀerence between the two? (c) Call the TL strategy proﬁle (1 plays T, 2 plays L)...

Question 4: Jar Game Consider the following game: Players: 2 - We designate player #1 to...

Question 4: Jar Game Consider the following game: Players: 2 - We designate player #1 to be the one that starts with the jar. Actions: - Each round at the same time both players deposit between 1 to 4 pennies into the jar. - Then both players are able to count the pennies in the jar. - If there are 21 or more pennies, the person with the jar is the winner. - If there are 20 or less pennies,...

Consider the situation below where two players are engaged in a game of chicken. In this...

Consider the situation below where two players are engaged in a game of chicken. In this game, both players drive their cars at each other and each player can choose to either drive straight, or swerve. If both cars drive straight, they will crash in to one another, causing damage to both vehicles. If one car goes straight, while the other swerves, the player that swerves is a "chicken" while the other player is respected for their bravery. If both...

5. Consider the following games played between two players, A and B. Game 1: A and...

5. Consider the following games played between two players, A and B. Game 1: A and B have reached a verbal agreement: A would deliver a case of beer to B, and B would deliver a bag of beer nuts to A. Now, each player needs to take an action: keep the promise (to deliver the goods), break the promise. If both keep their promises, then each player gets a payoff of 5; if both break their promises, then each...

Situations in life where game theory has been implicity or explcitly. What does game theory, implicity...

Situations in life where game theory has been implicity or explcitly. What does game theory, implicity & explicity mean? Please give examples.

Two players play a game where they start with a row of n piles of varied...

Two players play a game where they start with a row of n piles of varied amounts of money. The players take turns and in each turn a player can pocket either the money in the first pile or the last pile in the row of piles that remains. Design an efficient algorithm (using dynamic programming), which on any given sequence of amounts, determines the maximum amount of money that player 1 can win. If n is even, prove that...

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