4.6. A person purchases a dozen eggs and must take them home. Although making trips home is costless, there is a 50 percent chance that all of the eggs carried on one trip will be broken during the trip. This person con- siders two strategies: Strategy 1: Take the dozen eggs in one trip. Strategy 2: Make two trips, taking six eggs in each trip. a. List the possible outcomes of each strategy and the probabilities of these outcomes. Show that, on aver- age, six eggs make it home under either strategy. b. Develop a graph to show the utility obtainable under each strategy. c. Could utility be improved further by taking more than two trinc? How would a .

4.6. A person purchases a dozen eggs and must take them home. Although making trips home is costless, there is a 50 percent chance that all of the eggs carried on one trip will be broken during the trip. This person con- siders two strategies: Strategy 1: Take the dozen eggs in one trip. Strategy 2: Make two trips, taking six eggs in each trip. a. List the possible outcomes of each strategy and the probabilities of these outcomes. Show that, on aver- age, six eggs make it home under either strategy. b. Develop a graph to show the utility obtainable under each strategy. c. Could utility be improved further by taking more than two trinc? How would a .

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

Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 2 Strategy C D E F Player 1 A 9, 8 14, 14 18, 25 12, 19 B 23, 13 10, 18 14, 26 19, 21 a. What is player 1’s optimal strategy? multiple choice Strategy B Strategy A Player 1 does not have an optimal strategy. b. Determine player 1’s equilibrium payoff. Prev
5. The Stag Hunt is a famous coordination game where two hunters must work together to hunt a stag but each one has the option to go solo and hunt a hare. The following payoff matrix depicts such a game: a. b. Hunter A Stag Hare Stag 5,5 4,0 Hunter B Hare 0,4 4,4 List any pure strategy Nash equilibria if they exist. Does the game have a mixed strategy Nash equilibrium? If so, solve for it.
Please no written by hand solutions Consider a game between two friends, Amy and Brenda. Amy wants Brenda to give her a ride to the mall. Brenda has no interest in going to the mall unless her favorite shoes are on sale at the large department store there. Amy likes these shoes as well, but she wants to go to the mall even if the shoes are not on sale. Only Amy subscribes to the newspaper, which carries a daily advertisement of the department store. The advertisement lists all items that are on sale, so Amy learns whether or not the shoes are on sale by showing the newspaper to Brenda. But this is costly for Amy, because she will have to take the newspaper away from her sister, who will yell at her later for doing so. In this game, nature first decides whether or not the shoes are on sale, and this information is made known to Amy (Amy observes whether nature chose S or N). Nature chooses S with probability p and N with probability 1-p. Then Amy decides whether or not to take the…
Question 2. Two students are working together to submit their Microeconomics mid-semester group coursework. Each student i can put in the effort x; that costs c(x;), in which x; E [0, 1]. This gives each student the utility of u(x1, x2). Formu- late this situation as a strategic game.
4. Consider the two-player Rock-Paper-Scissors game. Each player can choose between three pure strategies: Rock, Paper, and Scissors. Strategy Rock beats Scissors, but loses to Paper. Strategy Paper beats Rock but loses to Scissors. Strategy Scissors beats Paper, but loses to Rock. When the game is a draw, the payoff for the players is '0'. The payoff of winning is ‘+1' and the payoff of losing is '-1'. Formulate this problem as a two-person, zero-sum game by constructing a payoff table.
Game Theory I am trying to assign numbers (theoretical)to a game im making. Its about Tipping. Its based on 3 different efforts a server has showed Can you assign numbers to each of these. This is all made up so you can use whatever values they just need to be in regard to the other values. Thanks. I was thinking to start on high effort Tip could be +10 and no tip could be -10 Best and worst scenario. You do high effort service and get tipped and high effort with no tip. Thanks
QUESTION 4 Suppose there are 2 players in a non- cooperative game theory situation. Player A can move Up or Down while Player B can choose Left or Right. The following matrix contains the payoffs that each player receives under 4 scenarios. The first number in each cell refers to the payoffs for Player A. Player A Up Down A. B. C. 10, 60 D. 20, 80 Player B Suppose Player A moves first and Player B moves second. There is one equilibrium, Up, Left Left There is one equilibrium: Down, Right. 50, 90 40, 50 There are two equilibria, (Down, Left) and (Up, Right) Right There is one equilibrium in this game, Up Right
5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…
4. Sonia the Terrible lands her ship and crew of scurvy-pirate raiders onto a foreign beach. Up on the headland is a village, led by Jen the Brave. At this point, Sonia has a choice: she can SLASH her water barrels, eliminating her water supplies; or she can NOT SLASH, which keeps her water supplies completely intact. Having seen the action taken by Sonia, Jen can choose to CHARGE or to WAIT. The payoffs are as follows: if Sonia the Terrible chooses to SLASH and Jen CHARGES, the payoffs are (100, 20) to Sonia and Jen, respectively. If Sonia SLASHES and Jen WAITS, the payoffs are (10, 30). On the other hand, if Sonia chooses to NOT SLASH and Jen CHARGES, the payoff is (20, 15). If Sonia opts to NOT SLASH and Jen chooses to WAIT, the payoffs are (40, 10), respectively. What is the subgame perfect (or credible) equilibrium outcome? a. Sonia the Terrible chooses to SLASH; Jen the Brave chooses to CHARGE b. Sonia the Terrible chooses to NOT SLASH; Jen the Brave chooses to WAIT c. Sonia the…
The 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…
1. Use the following game tree to answer parts a & b. At a chance node (Nature's turn) or when a player is indifferent between strategies, each branch has equal likelihood (50% chance they take either path). Nature receives no payoff. Assume players are mistake proof. Use a complete strategy when discussing the results of this game and provide a payoff, even if that payoff is an expected one. Recall that an expected payoff is the "average" payoff: for example if with 50% chance we receive a payoff of 5 and with 50% chance we receive a payoff of 2, the expected payoff is .5 x 5+ .5 x 2 = 3.5 a. What is the outcome of the game? Assume players are risk neutral (i.e., they see no difference in getting a payoff of 5 vs an expected payoff of 5). Red 0, 1, 3, 3 3, 2, 3, 2 Dorothy Blue Top 1, 4, 3, 2 Scarecrow 50% Green Nature Right Bottom 0, 2, 3, 1 Lion 50% 1, 3, 4, 2 3, 4, 3, 2 50% Left Nature 3, 2, 1, 2 Up 50% Red. 1, 3, 4, 2 Down Tinman Blue 0, 3, 3, 3 Yellow Dorothy 4, 3, 4, 2…
If you take a maximin strategy A. you are ensuring that the other player gets the worst possible outcome. B. you are irrational according to economic definition. C. then both players are doing the best they can given the payoffs in the game. D. you are getting the best possible outcome given that the other player does the thing that's worst for you.