Consider the following ultimatum game. In Stage 1, the proposer chooses a shares of $1 tooffer to the responder. The shares can be any number between 0 and 1 (including 0 and 1).After observing the proposer's decision, the responder may choose to accept or reject. If theresponder accepts, the proposer keeps (1 − s) × $1 and the responder receives s × $1. If theresponder rejects, both players receive 0. Assume that the responder always accepts when sheis indifferent between accepting and rejecting.Suppose that both the proposer (Player P) and the responder (Player R) exhibit inequityaversion as specified in the model of Fehr and Schmidt (1999), with ap = aR = 2 andẞp = ẞR = 0.6 (ap and ẞp are the parameters for player P; OR and BR are the parametersfor player R). Suppose these preferences are commonly known to both players. Use backwardinduction to solve the subgame perfect Nash equilibrium.

To solve for the subgame perfect Nash equilibrium (SPNE) using backward induction in the context of…

Answered: Consider the following ultimatum game.…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.12P

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Consider a modified version of the ultimatum game, with altruism. There is a pie of size 50 to be split between Proposer (P) and Responder (R). In the first stage, P offers a share 0 ≤ x ≤ 1 of the pie to R. In the second stage, R accepts or rejects P's offer. If R accepts, the pie is split according to the proposed division, with P receiving (1 - x) x 50 and R receiving x x 50. If R rejects, both players receive none of the pie. But players' payoffs are not equal to how much of the pie they receive. In particular, payoffs in the event of an accepted offer are: Up (1x) x 50+ bx × 50 UR = x x 50+b(1-x) × 50 (Payoffs in the event of a rejected offer are 0 for both players.) Here, the parameter b > 0 measures how altruistic players are, i.e. how much "happier" a player is when his opponent receives more pie. a) Suppose b = 0.5. How much pie does P receive in the subgame perfect Nash equilibrium of the game? (specify the total amount of pie, not the share). b) Suppose b=0.5. What is P's…
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.
Consider the following scenarios in the Ultimatum game, viewed from the perspective of the Recipient. Assume that the Recipient is motivated by negative reciprocity and will gain $15 of value from rejecting an offer that is strictly less than 50 percent of the total amount to be divided between the two players by the Proposer. Assume that the Proposer can only make offers in increments of $1. If the pot is $30, what is the minimum offer that the Responder will accept? What percent of the pie is this amount? The minimum offer that will be accepted is S. which represents percent of the pie. If the pot is $100, what is the minimum offer that the Responder will accept? What percent of the pie is this amount? The minimum offer that will be accepted is S, which represents percent of the pie. (Round answers to 2 decimal places as needed)
help please answer in text form with proper workings and explanation for each and every part and steps with concept and introduction no AI no copy paste remember answer must be in proper format with all working
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David wants to auction a painting, and there are two potential buyers. The value for eachbuyer is either 0 or 10, each value equally likely. Suppose he offers to sell the object for $6, and the two buyers simultaneously accept or reject. If exactly one buyer accepts, the object sold to that person for $6. If both accept, the object is allocated randomly to the buyers, also for $6. If neither accepts, the object is allocated randomly to the bidders for $0. (a) Identify the type space and strategy space for each buyer. (b) Show that there is an equilibrium in which buyers with value 10 always accept. (c) Show that there is an equilibrium in which buyers with value 10 always reject.
Consider the following voting game. There are three players, 1, 2 and 3. And there are three alternatives: A, B and C. Players vote simultaneously for an alternative. Abstaining is not allowed. Thus, the strategy space for each player is {A, B, C}. The alternative with the most votes wins. If no alternative receives a majority, then alternative A is selected. Denote ui(d) the utility obtained by player i if alternave d {A, B, C} is selected. The payoff functions are, u1 (A) = u2 (B) = u3 (C) = 2 u1 (B) = u2 (C) = u3 (A) = 1 u1 (C) = u2 (A) = u3 (B) = 0 a. Let us denote by (i, j, k) a profile of pure strategies where player 1’s strategy is (to vote for) i, player 2’s strategy is j and player 3’s strategy is k. Show that the pure strategy profiles (A,A,A) and (A,B,A) are both Nash equilibria. b. Is (A,A,B) a Nash equilibrium? Comment.
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.
The ultimatum game is a game in economic experiments. The first player (the proposer) receives a sum of money and proposes a fair proposal (F - 5;5) or unfair proposal (U - 8;2). The second player (the responder) chooses to either accept (A) or reject (R) this proposal. If the second player accepts, the money is split according to the proposal. If the second player rejects, neither player receives any money. 1 A 5:5 2 F R 0:0 U A 8:2 2 1. Find the subgame perfect Nash Equilibrium using backward induction. R 0;0
Consider 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.
Two friends are deciding where to go for dinner. There are three choices, which we label A, B, and C. Max prefers A to B to C. Sally prefers B to A to C. To decide which restaurant to go to, the friends adopt the following procedure: First, Max eliminates one of three choices. Then, Sally decides among the two remaining choices. Thus, Max has three strategies (eliminate A, eliminate B, and eliminate C). For each of those strategies, Sally has two choices (choose among the two remaining). a.Write down the extensive form (game tree) to represent this game. b.If Max acts non-strategically, and makes a decision in the first period to eliminate his least desirable choice, what will the final decision be? c.What is the subgame-perfect equilibrium of the above game? d. Does your answer in b. differ from your answer in c.? Explain why or why not. Only typed Answer
There are three players who must each choose an “effort” level from 1 to 7, that is, Si = {1, 2, 3, ..., 7}. The payoff for each player i is ui(si, s−i) = 10 max{s1, s2, s3} − si. How many pure- strategy Nash equilibria are there? Select one: a.2 b.4 c.none of the other answers d.3 e.1

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