A bunch of cookies should be divided among students by a teacher. Each student writes secretly on a sheet of paper his name and the amount of the cookies (his bid) he wants to get (other students cannot see this number). Then the teacher sorts these bids in ascending order and gives cookies to the students starting from the bid with the smallest amount. If cookies are finished at some point the rest of the students get nothing. If there are several equal bids that cannot be satisfied simultaneously with the current amount of cookies, cookies are equally divided among the students who named these bids. If there are extra cookies, the teacher keeps them. You should assume that cookies are perfectly divisible. Find a Nash Equilibrium in pure strategies. Explain why the set of strategies you propose is indeed a Nash Equilibrium in pure strategies. Explain why there are no other Nash equilibria.

A bunch of cookies should be divided among students by a teacher. Each student writes secretly on a sheet of paper his name and the amount of the cookies (his bid) he wants to get (other students cannot see this number). Then the teacher sorts these bids in ascending order and gives cookies to the students starting from the bid with the smallest amount. If cookies are finished at some point the rest of the students get nothing. If there are several equal bids that cannot be satisfied simultaneously with the current amount of cookies, cookies are equally divided among the students who named these bids. If there are extra cookies, the teacher keeps them. You should assume that cookies are perfectly divisible. Find a Nash Equilibrium in pure strategies. Explain why the set of strategies you propose is indeed a Nash Equilibrium in pure strategies. Explain why there are no other Nash equilibria.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Boris and Angela are negotiating a new trade deal, which resembles a modified centipede game. When it is their turn, each of them decides whether to cooperate (C) or to decline (D). Unfortunately, Angela is not sure how much time Boris has for the negotiations before he needs to leave to talk to Emmanuel. With probability p = 4/5, Boris will stay and insist on making the final proposal (long game, L). With probability 1 − p = 1/5, Boris will have to rush off, so that the game ends after Angela’s move (short game, S). Boris has perfect knowledge of his schedule. The structure and payoffs are represented in the game tree below (Attached picture). (a) Specify the set of possible histories H of the game. Underline terminal histories.(b) Specify the set of possible strategies for Boris and Angela.(c) How many subgames does this game have? Indicate all subgames in this game
The city council is to decide on a proposal to raise property taxes. Suppose Ms. Tuttle is the chair and the council’s other two members are Mr. Jones and Mrs. Doubtfire. The voting procedure works as follows: Excluding the chair, Mr. Jones and Mrs. Doubtfire simultaneously write down their votes on slips of paper. Each writes either for or against the tax increase. The secretary of the city council then opens the slips of paper and announces the vote tally. If the secretary reports that both slips say for, then the tax increase is implemented and the game is over. If both vote against, then the tax increase is not implemented and, again, the game is over. However, if it is reported that the vote is one for and one against, then Ms. Tuttle has to vote. If she votes for, then the tax increase is implemented, and if she votes against, then it is not. In both cases, the game is then over. As to payoffs, if the tax increase is implemented, then Mrs. Doubtfire and Mr. Jones each receive a…
Player 1 Cooperate (C) Defect (D) If the game has a dominant strategy, what is it? There is none. If the game has a Nash equilibrium in pure strategies, what is it? There is none. Cooperate (C) 3,3 8,0 Cooperate (C) is a dominant strategy for both players. Defect (D) is a dominant strategy for both players. Cooperate (C) is a dominant strategy for 1, and Defect (D) is a dominant strategy for 2. C, C is the only Nash equilibrium. D, D is the only Nash equilibrium. C, C and D, D are both Nash equilibria. Player 2 Defect (D) 0,8 1,1
The count is three balls and two strikes, and the bases are empty. The batter wants to maximize the probability of getting a hit or a walk, while the pitcher wants to minimize this probability. The pitcher has to decide whether to throw a fast ball or a curve ball, while the batter has to decide whether to prepare for a fast ball or a curve ball. The strategic form of this game is shown here. Find all Nash equilibria in mixed strategies.
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.
Finding Nash Equilibria Consider the following two player, normal form game: Player 1 Player 2 C L (2,1) U M (-2,-2) D R (2, -1) (1,2) (-1, 1) (0,0) (3,1) (0,0) (-1,-1) Find all pure and mixed strategy Nash equilibria. Calculate each player's expected payoffs at each equilibrium.
Channels 7 and 10 are the only television networks. They want to capture as much of the market as possible because it helps them earn more advertising revenue. Each channel can choose to show a cooking or a reality show on Sunday night. If they both airing cooking shows or both airing reality shows, Channel 10 gets 60% of the market. If Channel 10 is showing a cooking show and Channel 7 is showing a reality show, Channel 10 gets 70% of the market. If Channel 10 is showing a reality show and Channel 7 is showing a cooking show, Channel 7 gets 45% of the market. In a sequential game, Channel 7 moves first. What is true? Group of answer choices Channel 7 will choose reality. Channel 7 has a second mover advantage. Channel 10 will choose cooking. Channel 10 will choose reality. Channel 7 will choose cooking.
Consider the payoff matrix below, which describes a symmetric A B A 17,17 0,14 B 14,0 8,8 (a) Find all Nash equilibria of this game, including any mixed strategy equilibria. (b) Draw the expected payoff difference diagram for this game, including all the Nash equilibria you found in (a). is (c) What would you expect to occur most frequently when this game played as a lab experiment? Justify your answer using your answers from (a) and (b).
John and Paul are walking in the woods one day when suddenly an angry bear emerges from the underbrush. They each can do one of two things: run away or stand and fight. If one of them runs away and the other fights, then the one who ran will get away unharmed (payoff of 0) while the one who fights will be killed (payoff -200). If they both run, then the bear will chase down one of them and eat them to death but the other one will get away unharmed. Assuming they don't know which one will escape we will call this a payoff of -100 for both. If they BOTH fight, then they will successfully drive off the bear but they may be injured in the process (payoff -20). Construct a payoff matrix for this game and identify the pure strategy Nash equilibrium. (Indicate it with words not with a circle!)
Thelma and Louise are competitors in a local beer market and each is trying to decide if it is worthwhile to advertise. If both of them advertise, each will earn a profit of $2000. If neither of them advertises, each will earn a profit of $5000. If one advertises and the other doesn't, then the one who advertises will earn a profit of $7500 and the other will earn a profit of $1000. To make the most money, what should Thelma do and how much profit will she earn? Select one: a. she should advertise, and she will earn $7500 b. she should do whatever Louise does, and will earn either $2000 or $5000 C. she should not advertise, and she will earn $5000 d. she should advertise, and she will earn $2000 Next page
Define a new game as a modified version of the game in Problem 1, which we will call the Matching Two Pennies game: each player choose heads (H) or tails (T) for two pennies. In this game, Player 1 wins if both coins show the same combination of heads and tails, while Player 2 wins if they do not. (a) Write the strategy sets S1 and S2 for this game. (b) Give the payoffs for each player in this Matching Two Pennies game, by defining T;(81, 82) for each player and for each strategy pair, either as a list or in matrix form.
There is a city, which looks like a trapezoid, as shown below. Citizens liveuniformly distributed all over the city. Two ice-cream vendors, A and B, must independently set up stores in the city. Each citizen buys from the vendor closest to their location and when equidistant from both vendors they choose bycoin toss. Each vendor’s aim is to maximize the expected number of customers. A choice oflocation by the two vendors is a Nash equilibrium if no vendor can do better by deviatingunilaterally. Does this game have a Nash equilibrium? If so, describe it. If not, explain why not.