In the following game, identify how many subgames there are. Then, solve the game to find its subgame perfect Nash equilibrium. 1 L R 2 3,5 A B 1 W Y 2,1 5,2 1,3 4,4
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- A game theorist is walking down the street in his neighborhood and finds $20. Just as he picks it up, two neighborhood kids, Jane and Tim, run up to him, asking if they can have it. Because game theorists are generous by nature, he says he’s willing to let them have the $20, but only according to the following procedure: Jane and Tim are each to submit a written request as to their share of the $20. Let t denote the amount that Tim requests for himself and j be the amount that Jane requests for herself. Tim and Jane must choose j and t from the interval [0,20]. If j + t ≤ 20, then the two receive what they requested, and the remainder, 20 - j - t, is split equally between them. If, however, j + t > 20, then they get nothing, and the game theorist keeps the $20. Tim and Jane are the players in this game. Assume that each of them has a payoff equal to the amount of money that he or she receives. Find all Nash equilibria.At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1–4), noting the number showing. If the die shows a 3 and the coin shows tails, then you win $22. If the coin shows heads and the die shows an even number, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent.Which of the following games is simultaneous? - Monopoly - Chess - Checkers - 1-2-3 pass
- A certain game involves tossing 3 fair coins, and it pays 11cents for 3 heads , 7 cents for 2 heads, and 5cents for 1 head. Is 7 cents a fair price to pay to ply this game ? That is, does the 7 cents cost to play make the game fair?To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. $ (c) Is this game fair? Yes NoA researcher is conducting a DIFFERENT dictator game. In the first stage (S1), he forms pairs randomly and in each pair there is one dictator and one recipient. Each pair has $14 as endowment and a dictator has to decide how much to give to their recipient from the endowment. Then he adds another stage (S2) where it is stated that the dictators can give any amount between -$14 and +$14. a) explain what happens in Stage 1. b) explain what happens in stage 2. IN DETAIL
- Zara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game. Note: Sue only rolls a die once. The second roll, if the game goes up to that point, is made only by Zara.One day, Fred and his N friends were playing a card game in which each player throws a card with a number written on it. The cards are such that a number X is written on front of the card, and the negative of that number is written on the back side of the card. This game has the following rules: - Each of the N players is asked to throw a card. After all the N cards are thrown, Fred has to flip one or more cards in consecutive order, only orice. Your task is to help Fred flip the cards in such a way that the sum of the numbers, on front face of the cards, is the maximumConsider the following game of ’divide the dollar.’ There is a dollar to be split between two players. Player 1 can make any offer to player 2 in increments of 25 cents; that is, player 1 can make offers of 0 cents, 25 cents, 50 cents, 75 cents, and $1. An offer is the amount of the original dollar that player 1 would like player 2 to have. After player 2 gets an offer, she has the option of either accepting or rejecting the offer. If she accepts, she gets the offered amount and player 1 keeps the remainder. If she rejects, neither player gets anything. Draw the game tree.
- For the game described, if you want to break even in the long run, what should you pay for one play (for one roll of the die or one toss of the pair of coins)? (a) You receive one dollar for each dot on the uppermost face for one roll of a fair die. (b) You receive one dollar for each head on one toss of a pair of fair coms. (c) You receive one dollar for each dot on the uppermost face on one roll of a die which comes up five half the time, with the other faces equally likely.Ashleigh and Pavak play a game that begins with a pile of 100 toothpicks. They alternate turns with Ashleigh going first. On each player’s turn, they must remove 1, 3, or 4 toothpicks from the pile. The player who removes the last toothpick wins the game. Determine, with proof, which player has a winning strategy.Consider the following extensive form game: Find the subgame-perfect equilibrium for this game.