EBK MICROECONOMICS
2nd Edition
ISBN: 9780134458496
Author: List
Publisher: VST
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Question
Chapter 18, Problem 2P
To determine
Interpretation of an ultimatum game where the responder ends up negotiating for more or equal to half the share of money with the proposer.
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Suppose players A and B play a discrete ultimatum game where A proposes to split a $5 surplus and B responds by
either accepting the offer or rejecting it. The offer can only be made in $1 increments. If the offer is accepted, the
players' payoffs resemble the terms of the offer while if the offer is rejected, both players get zero. Also assume that
players always use the strategy that all strictly positive offers are accepted, but an offer of $0 is rejected.
A. What is the solution to the game in terms of player strategies and payoffs? Explain or demonstrate your answer.
B. Suppose the ultimatum game is played twice if player B rejects A's initial offer. If so, then B is allowed to
make a counter offer to split the $5, and if A rejects, both players get zero dollars at the end of the second round.
What is the solution to this bargaining game in terms of player strategies and payoffs? Explain/demonstrate your
answer.
C. Suppose the ultimatum game is played twice as in (B) but now there…
please only do: if you can teach explain each part
You could choose any position A (the first mover) or B (the second mover) in
the following three bargaining games. For each game (I, II, or III), explain which
player (A or B) you would pick in order to maximize your expected payoff?
1. Game I (one stage): A will make the first move and offer her partner a portion
of 6 dollars. If the offer is accepted, the bargain is complete and each player gets an
amount determined by the offer. If the offer is declined, each player gets nothing.
2. Game II (two stages): A will make the first move and offer her partner
a portion of 12 dollars. If the offer is accepted, the bargain is complete and each
player gets an amount determined by the offer. If the offer is declined, the 12 shrinks
to 5 and B then gets a turn to make an offer. Again, the bargain is complete if A
accepts and the division is made according to the terms of the offer. If player A
declines the offer, each player gets nothing.
3. Game III (three stages): A will make the first move…
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Similar questions
- Boris and Leo are playing an ultimatum bargaining game, with £1000 to share. Boris is the proposer. Suppose Leo has the following preferences: his utility in monetary terms is the amount of money he gets minus 40 percent of Boris's amount Which of the following statements is/are correct? a) If Leo's preferences change so that his utility in monetary terms were the amount of money he gets minus 100 percent of Boris's amount, his minimum acceptable offer would increase. b) The minimum offer Leo will accept is larger than £250. c) The description of Leo's preferences suggest that Leo is altruistic.arrow_forwardplease if you can teach explainarrow_forwardSuppose Justine and Sarah are playing the ultimatum game. Justine is the proposer, has $140 to allocate, and Sarah can accept or reject the offer. Based on repeated experiments of the ultimatum game, what combination of payouts to Justine and Sarah is most likely to occur?.arrow_forward
- In 'the dictator' game, one player (the dictator) chooses how to divide a pot of $10 between herself and another player (the recipient). The recipient does not have an opportunity to reject the proposed distribution. As such, if the dictator only cares about how much money she makes, she should keep all $10 for herself and give the recipient nothing. However, when economists conduct experiments with the dictator game, they find that dictators often offer strictly positive amounts to the recipients. Are dictators behaving irrationally in these experiments? Whether you think they are or not, your response should try to provide an explanation for the behavior.arrow_forwardConsider the following game - one card is dealt to player 1 ( the sender) from a standard deck of playing cards. The card may either be red (heart or diamond) or black (spades or clubs). Player 1 observes her card, but player 2 (the receiver) does not - Player 1 decides to Play (P) or Not Play (N). If player 1 chooses not to play, then the game ends and the player receives -1 and player 2 receives 1. - If player 1 chooses to play, then player 2 observes this decision (but not the card) and chooses to Continue (C) or Quit (Q). If player 2 chooses Q, player 1 earns a payoff of 1 and player 2 a payoff of -1 regardless of player 1's card - If player 2 chooses continue, player 1 reveals her card. If the card is red, player 1 receives a payoff of 3 and player 2 a payoff of -3. If the card is black, player 1 receives a payoff of 2 and player 2 a payoff of -1 a. Draw the extensive form game b. Draw the Bayesian form gamearrow_forwardConsider the following game: you and a partner on a school project are asked to evaluate the other, privately rating them either "1 (Good)" or "0 (Bad)". After all the ratings have been done, a bonus pot of $1000 is given to the person with the highest number of points. If there is a tie, the pool is split evenly. Both players only get utility from money. Mark all of the following true statements: A. The best response to your partner rating you as Good is to rate them as Good as well. Your answer B. There is no best response in this game. C. Your partner's best response to you rating them as Bad is to also rate you as C Bad. D. Your best response to any strategy of your partner is to play "Good".arrow_forward
- Consider a variant of the ultimatum game we studied in class in which players have fairness considerations. The timing of the game is as usual. First, player 1 proposes the split (100 – x, x) of a hundred dollars to player 2, where x € [0, 100]. Player 2 observes the split and decides whether to accept (in which case they receive money according to the proposed split) or reject (in which case they both get 0 dollars). But now player i's utility equals to her monetary utility minus the disutility from unfairness proportional to the difference in the monetary outcomes. That is, given a final split (m1, m2), let u1(m1, m2) = m1 – B1(m1 -– m2)² u1(m1, m2) = m2 - B2(m1 – m2)², where B1, B2 are parameters of the game indicating how strongly players care about fairness. Note that the case we considered in class corresponds to ß1 = B2 = 0.arrow_forwardAmir and Beatrice play the following game. Amir offers an amount of money z € [0, 1] to Beatrice. Beatrice can either accept or reject. If Beatrice accepts, then Amir receives 1 - z dollars and Beatrice receives a dollars. If Beatrice rejects, then both receive no money. As in the Ultimatum Game, Amir cares only about maximizing the amount of money he receives. Beatrice, on the other hand, detests Amir, and therefore cares about the amount of money that both receive: if Amir receives y dollars and Beatrice receives a dollars, then Beatrice's payoff is a-ay where a > 0. (a) Find all pure strategy Nash equilibria of the game in which the two players choose simultaneously (thus Beatrice accepts or rejects without seeing Amir's offer). Solution: The NE are the strategy profiles in which Beatrice rejects and Amir's offer a satisfies 2-a(1-x) ≤0, i.e. r ≤a/(1+a). (b) Find all subgame perfect equilibria of the sequential game in which Amir first makes the offer and Beatrice observes the offer…arrow_forwardConsider an odd type of student who prefers to study alone except when the group is large. We have four of these folks: Melissa, Josh, Samina, and Wei. Melissa and Josh are deciding between studying in the common room in their dorm (which we will denote D) and the library (denoted L). Samina and Wei are choosing between the library and the local cafe (denoted C). If someone is the only person at a location, then his or her payoff is 6. If he or she is one of two people at a location, then the payoff is 2. If he or she is one of three people, then the payoff is 1. If all four end up together, then the payoff is 8.a. Is it a Nash equilibrium for Melissa and Josh to study in the commonroom and for Samina and Wei to study in the cafe?b. Is it a Nash equilibrium for Josh to study in the common room, Saminato study in the cafe, and Melissa and Wei to study in the library?c. Find the Nash equilibria.arrow_forward
- Find the SPNE for the centipede game. Centipede game: Two players, 1 and 2, take turns choosing one of two actions each time, continue or stop. They both start with $1 in their respective piles, and each time i says continue, $1 is taken away from his pile, and $2 are added to the other player's pile. The game automatically stops when both players have $100 in their respective piles.arrow_forwardImagine two drivers playing chicken, a game where they drive towards one another with their cars. Each driver has two actions: go straight or turn left. For simplicity, we standardize directions according to the perspective of an overhead observer. Thus, if both drivers select the same action, they will crash. At the same time, each driver wants to go straight, to seem tough and fearless. Utilities are given by the following table: Utility Turn Left Straight Turn Left -20, -20 - 5, 10 Straight 10, -5 -10, -10 These are in the format (row player, column player) 1. Does either player have a dominating strategy? If so, identify all of them. 2. What are the pure strategy Nash equilibria of this game? 3. Does the game have any mixed strategy Nash equilibria? If yes, compute all of them.arrow_forwardThe chicken game has often been used to model crises. Recall that in this game, the two players drive straight at each other. They can choose to swerve or keep going straight. If one swerves, and the other goes straight, assume that the one that swerves gets -10 utility and the one that goes straight gets 10 utility, since the one that swerves is deemed the loser. If both swerve, both get 0 utility. If both go straight, they crash and get -50 utility. Assume both players have a discount rate of 0.9 Draw the stage game of date night List all pure strategy Nash equilibria of the single stage game Consider an infinite horizon version of Chicken. Can you get an SPNE in which the both players swerve using a grim trigger type strategy? Consider the following strategies: both players swerve, as long as neither ever went straight. If one player ever plays straight, in all subsequent rounds the player that swerved goes straight and the player that went straight swerves. Can you think…arrow_forward
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