3. Noah and Xaviera love to play "Hide and Seek." It is a simple game, but it continuesto amuse. It goes like this. Xaviera hides upstairs or downstairs. Noah can lookupstairs or downstairs but not in both places. If he finds Xaviera, Noah gets one scoopof ice cream and Xaviera gets none. If he does not find Xaviera, Xaviera gets onescoop of ice cream and Noah gets none.a. Fill in the payoffs in the matrix below! Is this a zero-sum game? What are theNash equilibria in pure strategies?Hide and SeekXavieraUpstairsDownstairsUpstairsNoahDownstairsb. Find a Nash equilibrium in mixed strategies for this game.c. Noah and Xaviera made new rules for this game. Now if Noah finds Xavieraupstairs, he gets two scoops of ice cream, but if he finds her downstairs, hegets one scoop. If Noah finds Xaviera, she gets no ice cream, but if he doesn'tfind her she gets one scoop. Fill in the payoffs in the graph below! Are thereany Nash equilibria in pure strategies?Advanced Hide and SeekXavieraUpstairsDownstairsUpstairsNoahDownstairsd. What mixed strategy equilibrium can you find?

Given information set 2 players: Noah and Xavier 2 set of strategy for each player: Upstairs,…

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

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

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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9. In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player 2 is described as follows: ⚫ There are two "statuses" that player i might be in during any period: "normal" and "revenge"; • In a normal status player i cooperates; ⚫ In a revenge status player i defects; • From a normal status, player i switches to the revenge status in the next period only if the other player defects in this period; • From a revenge status player i automatically switches back to the normal status in the next period regardless of the other player's action in this period. Consider an infinitely repeated game so that with probability p that the game continues to the next period and with probability (1-p) it ends. Cooperate (C) Defect (D) Cooperate (C) 4,4 5,0 Defect (D) 0,5 1,1 What is the threshold p* such that when p≥ p* always cooperating by player 2 is a best response to player 1 playing tit for tat and starting in a normal status, but when p < p*…
RUSH. Answer for a, b, and c.
2. Suppose that Ann and Bob play a two-person game with payoffs A (for Ann) and CB (for Bob). Bob's utility is UB (XA, XB) = XB o max{2B – £A;0} − pmax{2A – TB;0} (a) Describe Bob's utility function. Explain the meaning of the two parameters p and o, and why they might differ. Do you think that it is more natural for p to be larger than o or not, and why? J (b) Ann and Bob play an ultimatum bargaining game: Bob has an endowment of 10 experimental unit and he has to decide how many experimental unit he would like to assign to Ann. Ann can either accept or reject. If she accepts, then the allocation that Bob proposes is implemented; if she rejects they both get zero and the game is over. i. Explain what is the likely outcome of this game if Ann and Bob have selfish preferences. ii. Explain how the outcome may differ if Bob is inequity averse and Ann is selfish. iii. Now assume, for simplicity, that Bob has only two possibilities: he either offers an equal split, or he keeps all the…
Mohamed and Kate each pick an integer number between 1 and 3 (inclusive). They make their choices sequentially.Mohamed is the first player and Kate the second player. If they pick the same number each receives a payoff equal to the number they named. If they pick a different number, they get nothing. What is the SPE of the game? a. Mohamed chooses 3 and Kate is indifferent between 1, 2 and 3. b. Mohamed chooses 3 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2, and 3 if Mohamed chooses 3. c. Mohamed chooses 1 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2 and 3 if Mohamed chooses 3. d. Mohamed chooses 3 and Kate chooses 3.
2. Consider two players playing a simultaneous moves game. These players can be one of the two states of the world, state 1 or state 2, while playing the game. The payoffs-matrix for the two state games are as follows: State 1 P1 U D P2 L R 1,4 1,0 1,6 2,16 0,0 0,24 M State 2 P1 U D P2 L M R 1,0 1,4 1,6 2,16 0,24 0,0 Each players believes that the two states are equally likely, Derive the BNE of the game.
Rita is playing a game of chance in which she tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random. This game is this: Rita tosses the dart once. She wins $1 if the dart lands in slice 1, $2 if the dart lands in slice 2, $5 if the dart lands in slice 3, and $8 if the dart lands in slice 4. She loses $3 if the dart lands in slices 5, 6, 7, or 8. (If necessary, consult a list of formulas.) (a) Find the expected value of playing the game. | dollars (b) What can Rita expect in the long run, after playing the game many times? O Rita can expect to gain money. She can expect to win dollars per toss. Rita can expect to lose money. She can expect to lose dollars per toss. O Rita can expect to break even (neither gain nor lose money).
2. There are two ice-cream stores, each of whom chooses a position from ten spots along the beach: spot 1, 2, 3, ...10. The ten spots are lined up and separated 100 meters from each other. 1 2 3 4 5 6 7 8 9 10 The consumers are equally distributed across these ten spots. Consumers buy from the store whose spot is closest to theirs. If the two stores are equidistant from a given spot, the consumers at that position split their consumption equally. The aim of the ice-cream stores is to maximize their share of the total ice-cream consumption. a. Is there any dominated strategy? If so, spell out explicitly how one strategy is dominated by another strategy. b. Is there any iterated dominance equilibrium?
Assume the following game situation: If Player A plays UP and Player B plays LEFT then Player A gets $1 and Player B gets $3. If Player A plays UP and Player B plays RIGHT then Player A gets $2 and Player B gets $5. If Player A plays DOWN and Player B plays LEFET then Player A gets $4 and Player B gets $2. If Player A plays DOWN and Player B plays RIGHT then Player A gets $1 and Player B gets $1 What is the Mixed Strategy Equilibrium for Player B? O. (LEFT, RIGHT) = (1/8, 3/8) O. (LEFT, RIGHT) = (1/4, 3/4) O. (LEFT, RIGHT) = (1/2, 1/2) O. (LEFT, RIGHT) = (3/8, 1/8)
6. Eventually, Aron and Nora who we met in the previous problem were able to get together and have now been an item for some time. So long, in fact, that there are issues. Aron is a little insecure, which makes him jealous. Nora is none too pleased about it. When she arranges a girls' night out with some of her friends, Aron is very upset and threatens to break up. So Nora has to decide to go out with her friends or stay home with Aron. If she stays home, she gets a payoff of 0, whereas Aron gets what he wants and a payoff of 2 (perhaps he should be a little more concerned with Nora's happiness). On the other hand, if Nora decides to go out, then Aron must make a choice between breaking up or not. If he breaks up, both he and Nora are miserable and each receives a payoff of -1. If he does not, he gets a payoff of 1 while Nora gets what she wants and a payoff of 2. a) Draw the extensive form of this game. b) Find all Nash equilibria. Explain your answer carefully. c) Find the backward…
Consider the game between CrossTalk vs GlobalDialog in the attached file. The number of pure strategies of CrossTalk is Blank 1. Fill in the blank, read surrounding text. , and the number of pure strategies of GlobalDialog is Blank 2. Please answer Blank1 and 2 GlobalDialog 14 High Don't Invest 1 GlobalDialog Don't 0,0 0,- Low 6. Invest -,0 GlobalDialog 2 1 High Low 14 High High 2,2 -10,6 CrossTalk Low Low 6, –10 -2,–2 6. CrossTalk CrossTalk
Below is an example of which game? A1 C D C get out and Both prisoners split the loot. Al goes free and keeps all the loot; A2 goes to jail. A2 O Chicken D Al goes to jail; A2 goes free and keeps all the loot. Both go to jail and split the loot later. O Stag Hunt O Prisoner's Dilemma O Cooperation A1 C D C 3,3 4,1 A2 D 1,4 2,2*
3. Blackadder and Baldrick are rational, self-interested criminals imprisoned in separate cells in a dark medieval dungeon. They face the prisoner's dilemma displayed in the matrix. Assume that Blackadder is willing to pay $1,000 for each year by which he can reduce his sentence below 20 years. A corrupt jailer tells Blackadder that before he decides whether to confess or deny the crime, she can tell him Baldrick's decision. How much is this information worth to Blackadder? (LO2) Blackadder Confess Deny O for Baldrick Confess 5 years for each 20 years for Blackadder Baldrick 20 years for Baldrick Deny 1 year for each O for Blackadder