(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.)
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 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 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.
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 = 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 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 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 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...
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...