Finite Mathematics (11th Edition)
11th Edition
ISBN: 9780321979438
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 11.2, Problem 26E
(a)
To determine
The value of game matrix to be determined from optimal strategy.
(b)
To determine
The value of game matrix to be determined from optimal strategy.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A game theorist is walking down the street in his neighborhood and finds $20. Just as he picks it up, two neighborhood kids, Jane and Tim, run up to him, asking if they can have it. Because game theorists are generous by nature, he says he’s willing to let them have the $20, but only according to the following procedure: Jane and Tim are each to submit a written request as to their share of the $20. Let t denote the amount that Tim requests for himself and j be the amount that Jane requests for herself. Tim and Jane must choose j and t from the interval [0,20]. If j + t ≤ 20, then the two receive what they requested, and the remainder, 20 - j - t, is split equally between them. If, however, j + t > 20, then they get nothing, and the game theorist keeps the $20. Tim and Jane are the players in this game. Assume that each of them has a payoff equal to the amount of money that he or she receives. Find all Nash equilibria.
A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.a. What are p0, p1, n, and c for this problem?
Solve the following game graphically. The payoff is for Player A.
B1
B2
B3
A1
2
-3
8
A2
3
3
-6
Chapter 11 Solutions
Finite Mathematics (11th Edition)
Ch. 11.1 - In the following game, decide on the payoff when...Ch. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - In the following game, decide on the payoff when...Ch. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Does it have a saddle point?Ch. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - APPLY IT Football When a football team has the...Ch. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Children's Game In the children's game rock,...Ch. 11.2 - Suppose a game has payoff matrix [ 3452 ]. Suppose...Ch. 11.2 - Suppose a game has payoff matrix [ 041324110 ]....Ch. 11.2 - Find the optimum strategies for player A and...Ch. 11.2 - Find the optimum strategies for player A and...Ch. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - A reader wrote to the "Ask Marilyn" column in...Ch. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Choosing Medication The number of cases of African...Ch. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - 37. Golf In a simplified variation of the Ryder...Ch. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Finger Game Repeal Exercise 40 if each player may...Ch. 11.3 - Use the graphical method to find the optimum...Ch. 11.3 - Prob. 2ECh. 11.3 - Use the graphical method to find the optimum...Ch. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Use the simplex method to find the optimum...Ch. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - In Exercises 1327, use the graphical method when...Ch. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - In Exercises 1327, use the graphical method when...Ch. 11.3 - In Exercises 13–27, use the graphical method when...Ch. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11 - 1. Since they like to eat out, each prefers a...Ch. 11 - If Linda likes French food more than Mel likes...Ch. 11 - Prob. 3EACh. 11 - 4. Suppose Linda knows that Mel is going to stick...Ch. 11 - Prob. 5EACh. 11 - Prob. 6EACh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - 11. How can you determine from the payoff matrix...Ch. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - For the following games, find the strategies...Ch. 11 - Prob. 27RECh. 11 - For the following games, find the strategies...Ch. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - For each game, remove any dominated strategies,...Ch. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Labor Relations In labor-management relations,...Ch. 11 - Prob. 48RECh. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Politics Mary Wilkinson, a candidate for city...Ch. 11 - Prob. 56RECh. 11 - Prob. 57RECh. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - Prob. 60RECh. 11 - Prob. 61RECh. 11 - Prob. 62RECh. 11 - Prob. 63RECh. 11 - Newcomb's Paradox Suppose there are two boxes, A...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- nternet Audience At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 22 x + y = 44 + z + u and x − y + z − u = 46. How large was the audience of each of the four companies at the end of that year? MicrosoftTime WarnerYahooGooglearrow_forwardJo, a store owner, has an option of selling hot drinks or halu-halo during a championship game. The profits will depend on weather conditions. On a clear day, the profits will be P 1,500 and P9,000 on a rainy day if she sells hot drinks. If she sells halu-halo, her profits will be P 10,000 on a clear day and P5,000 an a rainy day. It was learned that during the time of the year 65% of the days are clear and 35%) are rainy. What type of refreshments should the owner sell? Make a decision tree and state your decision.arrow_forwardConsider a symmetric game with 10 players. Each player chooses among three strategies: x, y, and z. Let nx denote the number of players who choose x, ny denote the number of players who choose y, and nz denote the number of players who choose z. (So, nz = 10−nx−ny.) The payoff to a player from choosing strategy x is 10−nx (note that nx includes this player as well), strategy y is 13−2ny (again ny includes this player as well), and strategy z is 3. (a) Show that a Nash equilibrium must have at least one person choosing x and at least one person choosing y. (Hint: In a Nash equilibrium, no player can do better by doing something different.) b) Find all Nash equilibria.arrow_forward
- If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using MAXIMAX CRITERION? D1 D2 D3 D4 What decision alternative will he choose if using MAXIMIN CRITERION? D1 D2 D3 D4 What about MINIMAX REGRET CRITERION? D1 D2 D3 D4 What decision would he make if using criterion of realism at alpha 0.6 is used? D1 D2 D3 D4arrow_forwardThree marksmen Tom, Joe, and Bill are aiming at three targets, T1, T2, T3. Tom will choose either target T1 or T2, with p=0.5 of choosing T1, and p=0.5 of choosing T2. Joe will choose either target T2 or T3, with p=0.5 of choosing T2, and p=0.5 of choosing T3. Bill will randomly choose either target T1 or T3, with p=0.5 of choosing T1, and p=0.5 of choosing T3. Also, the probability of each marksman hitting their chosen target is p=0.6 for Tom, p=0.6 for Joe, and p=0.3 for Bill. A hit is registered if a target is hit by any marksman. Let X denote the number of targets that are hit after all three take one shot at the same time. a) What is the probability that T1 is hit after one round of fire? b) Find E[X] (A diagram is attached to aid with maksmen/target layout)arrow_forwardFor the game described, if you want to break even in the long run, what should you pay for one play (for one roll of the die or one toss of the pair of coins)? (a) You receive one dollar for each dot on the uppermost face for one roll of a fair die. (b) You receive one dollar for each head on one toss of a pair of fair coms. (c) You receive one dollar for each dot on the uppermost face on one roll of a die which comes up five half the time, with the other faces equally likely.arrow_forward
- Empirical data suggests that subjects do better than predicted by game theory at (A) signalling and coordination; (B) backward induction; (C) mixing their strategies; (D) none of the above.arrow_forwardIn a particular class, exams are worth 50%50% of the overall grade, quizzes are worth 30%30% of the overall grade, homework is worth 15%15% of the overall grade, and class participation is worth 5%5% of the overall grade. A particular student has earned an average score of 82.2%82.2% on the exams, 76.3%76.3% on the quizzes, 90.0%90.0% on the homeworks, and 100.0%100.0% on class participation. What is this student's overall grade in the course? Report the answer with one digit after the decimal point. overall grade:arrow_forwardIn a game, a participant is given three attempts to hit a ball. On each try, she either scores a hit, H, or a miss, M. The game requires that the player must alternate which hand she uses in successive attempts. That is, if she makes her first attempt with her right hand, she must use her left hand for the second attempt and her right hand for the third. Her chance of scoring a hit with her right hand is .7 and with her left hand is .4. Assume that the results of successive attempts are independent and that she wins the game if she scores at least two hits in a row. If she makes her first attempt with her right hand, what is the probability that she wins the game?arrow_forward
- Suppose O1 is twice as likely as O4, O1 is equally as likely as O2, O5 is 5 times as likely as O2, and Pr[O3]=1/3. Find Pr[O5]arrow_forwardif w = 6 (a) This game has a unique (pure strategy) Nash equilibrium ⟨t*1 , t*2 ⟩ in which t*1 = t*2 Find the value of t*1 . (If your answer is a fraction, report it in lowest terms.) (b) To which strategy t2 is the strategy t1 = 4 a best response? (If your answer is a fraction, report it in lowest terms.)arrow_forwardConsider a two-player game that is set up with two piles of stones. The two players are taking turns removing stones from one of the two piles. In each turn, a player must choose a pile and remove one stone or two stones from it. The player who removes the last stone (making both piles empty) wins the game. Show that if the two piles contain the same number n ∈ Z+ of stones initially, then the second player can always guarantee a win.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Graph Theory: Euler Paths and Euler Circuits; Author: Mathispower4u;https://www.youtube.com/watch?v=5M-m62qTR-s;License: Standard YouTube License, CC-BY
WALK,TRIAL,CIRCUIT,PATH,CYCLE IN GRAPH THEORY; Author: DIVVELA SRINIVASA RAO;https://www.youtube.com/watch?v=iYVltZtnAik;License: Standard YouTube License, CC-BY