Figure 12.5 Consider Figure 12.5. The dominant strategy in the prisoners' dilemma is: O A. to confess for both players. OB. to confess for player A but not to confess for player B. OC. not to confess for both players. O D. to confess for player B but not to confess for player A.
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- 12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?L 0 4 15.1 X₂ A M R 0 1 4 0 2 B L 4 0 с X3 M R 0 1 3 FIGURE 15.5 Exercise 15.1. Equilibrium Selection: Consider the extensive-form game in Figure 15.5. a. Find all the Bayesian Nash equilibria of this game. b. Which of the Bayesian Nash equilibria are also perfect Bayesian equi- libria? Why?In game theory, a dominant strategy is the best strategy to pick, no matter which moves are chosen by the other player. O to make the exact same move that was made by the other player. the choice that causes the payoff for the other player to be minimized, regardless of the payoff it earns the best strategy to pick, assuming the other player makes his or her best possible choice. to allocate all personnel resources towards defensive talent in order to dominate opposing offenses. 46°F
- learn.canterbury.ac.nz Clasarsom Nov 15-ICO EUC LEARN | AKO See the game below and answer the questions 8 to 11: Player-1 C Player-2 X, Y Y Player-1 9 14 8. Player-2 16 17 16 Nash Equilibrium in this game: Select one: O a. Playert: C; Player2: X O b. Playert: C; Player2: Y Oc. Playert: L; Player2: X Od. Playert: L; Player2: Y e. None1. Consider the following sequential game: Left (3,5) Mary Go (6,4) Up Right John Stop (5.7) John (a) Draw the game tree of the game. John Go Down (4,1) Left Mary Stop (2,5) Right (6,-1) (John as player 1 and Mary as player 2) By backward induction, find a Nash equilibrium and the corresponding payoffs. 2. Eve and Noa start with $10 in each of their piles. They take turns choosing one of two actions, continue or stop, with Eve choosing first. Each time a player says continue, $10 will be removed from her pile, and $20 will be added to the other player's pile. The game automatically stops when the total amount in their piles reaches $60. (Eve as player 1 and Noa as player 2) (b) By backward induction, find a Nash equilibrium and the corresponding payoffs.Mark and Bevis play a static game. Mark chooses x and Bevis chooses y. Mark's payoff is 16 - (x- y)2, and Bevis' payoff is 16 - (x-0.5)2 - (y-0.5)2. Then O a. both Mark and Bevis have dominant strategies O b. Mark has a dominant strategy, but Bevis does not O c. Bevis has a dominant strategy, but Mark does not O d. neither Mark or Bevis have dominant strategies
- Question 24 In the coordination game shared in class and in the textbook, it shows players Alex and Tyler coordinating over using Microsoft or Apple software. The strategies lead to a situation with two Nash Equilibria where both use Microsoft or both use Apple with each associated with different equal payoffs. This game is illustrating which concept of Network Goods? O The contestability of the market for a network good. O The "best" product may not win. O The coordination amongst competing network goods. O The required scale of success in the market.1. Suppose the following prisoner's dilemma is played twice with the payoff for the entire game being the sum of the payoffs from the two stages. Assume there is no discounting. Player 1 B Player 2 B 2,6 3,3 A 5,5 6,2 a. What is the Nash equilibrium for stage two? b. Show what the game in stage 1 amounts to when the players anticipate the Nash equilibrium for stage 2. c. Provide the subgame-perfect outcome for this game.Game Theory. 1. Yuppie town has two food stores, LA Boulangerie, which sells bread, and La Fromagerie, whichsells cheese. It costs $1 to make a loaf of bread and $2 to make a pound of cheese. If LaBoulangerie's price is P 1 dollars per loaf of bread and La Fromagerie's price is P 2 dollars per pound ofcheese, their respective weekly sales, Q 1 thousand loaves of bread and Q 2 thousand pounds ofcheese, are given by the following equations: a) For each store, write its profits as a function of P 1 and P 2 , and find the Nash equilibriumprices in this game. b) Suppose that the two stores collude and set prices jointly to maximize the sum of theirprofits. Find the joint profit-maximizing prices for the stores.c) Provide an explanation for the differences between the Nash equilibrium prices and thosethat maximize joint profits.
- 6. The owner of an antique piece of furniture is looking to sell their good to a known buyer. The seller has a reservation value r whereas the buyer has valuation v > r. Suppose the buyer incurs a one-off transportation cost of t from travelling to the seller to purchase the good. Assume that r, vand t are known to both parties. The game proceeds in two stages: First, the buyer decides whether or not to travel to the seller's location in order to purchase. Second, if they travel then the seller makes a take-it-or-leave-it offer (ultimatum) of price p to the buyer, which the buyer then can either accept or reject. (a) Represent this game in extensive form (b) Find the seller's optimal offer in Stage 2 of this game given that the buyer has already travelled. Is it accepted or rejected? (c) Find a Subgame Perfect Equilibrium of this game. (d) Are there any Nash equilibria which are not subgame perfect? Give an example if one exists. (e) Suppose the seller could offer free delivery at a…20.38 C 1 Search il 4G O Microeconom... 1. In the sequential games such as the sequential Battle of the Sexes, why does the Nash equilibrium allow for outcomes with noncredible threats? 2. Left Right Up 1, 3 3, 1 Down 2, 2 4, 4 a. Find the Nash equilibrium or equilibria b. Which player, if any, has a dominant strategy? c. Does A benefit from changing the game by reducing his or her payoff in this way? 3. Noah and Xaviera love to play "Hide and Seek." It is a simple game, but it continues to amuse. It goes like this. Xaviera hides upstairs or downstairs. Noah can look upstairs or downstairs but not in both places. If he finds Xaviera, Noah gets one scoop of ice cream and Xaviera gets none. If he does not find Xaviera, Xaviera gets one scoop of ice cream and Noah gets none. a. Fill in the payoffs in the matrix below! Is this a zero-sum game? What are the Nash equilibria in pure strategies? Hide and Seek Xaviera Upstairs Downstairs Upstairs Noah Downstairs b. Find a Nash equilibrium in…You are playing a game with a friend. It’s yourmove but you don’t have a dominant strategy.Your payoff depends on what your friend doesafter your move. You consider flipping a coin todecide what to do. You are about to reach for acoin, but then you realize that your friend has adominant strategy. Explain how using backwardinduction (rather than a coin toss) will now determine your next move
