Finite Mathematics & Its Applications (12th Edition)
12th Edition
ISBN: 9780134437767
Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
Publisher: PEARSON
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Chapter 9.3, Problem 11E
To determine
To calculate: The value of the game and optimal strategy for R and C for the payoff matrix,
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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.
a.Discuss five assumptions of game theory
b.Explain three steps required to find a saddle point
if Z = 3
(a) How many pure strategy profiles exist in this game?
(b) In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs to the two players?
Chapter 9 Solutions
Finite Mathematics & Its Applications (12th Edition)
Ch. 9.1 - Solutions can be found following the section...Ch. 9.1 - Prob. 2CYUCh. 9.1 - Prob. 3CYUCh. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - Prob. 7E
Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - In Exercises 112, determine the optimal pure...Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - For each of the games that follow, give the payoff...Ch. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.2 - Solutions can be found following the section...Ch. 9.2 - Prob. 2CYUCh. 9.2 - Prob. 1ECh. 9.2 - Suppose that a game has payoff matrix [102120011]...Ch. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Flood Insurance A small business owner must decide...Ch. 9.2 - 7. Two players, Robert and Carol, play a game with...Ch. 9.2 - Rework Exercise 7 with [.7.3] as Roberts strategy.Ch. 9.2 - Two players, Robert and Carol, play a game with...Ch. 9.2 - 10. Rework Exercise 9 with as Robert’s...Ch. 9.2 - 11. Assume that two players, Renée and Carlos,...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - 16. Three-Finger Morra Reven and Coddy play a game...Ch. 9.3 - Prob. 1CYUCh. 9.3 - Prob. 2CYUCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - In Exercises 5–12, determine the value of the game...Ch. 9.3 - In Exercises 512, determine the value of the game...Ch. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - In Exercises 13–16, determine the value of the...Ch. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Football Suppose that, when the offense calls a...Ch. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Three-Finger Mor ra Reven and Coddy play a game in...Ch. 9.3 - Advertising Strategies The Carter Company can...Ch. 9 - 1. What do the individual entries of a payoff...Ch. 9 - Prob. 2FCCECh. 9 - Prob. 3FCCECh. 9 - Prob. 4FCCECh. 9 - Prob. 5FCCECh. 9 - Prob. 6FCCECh. 9 - Prob. 7FCCECh. 9 - What is meant by the optimal mixed strategies of R...Ch. 9 - In Exercises 14, state whether or not the games...Ch. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 3PCh. 9 - Prob. 4PCh. 9 - Prob. 5PCh. 9 - Prob. 6P
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- The Chinese government has created a fund worth more than 20 trillion won to foster the semiconductorindustry. Although there is a large technological difference between memory semiconductors, systemsemiconductors can be developed in a short period of time. The number of companies producinghomogeneous quality products has increased.■Question (a) In the Cournot game, when the number of firms increases from 2 to n, compare the output,total output, and profit of each firm with N.E. in the Cournot model. ■Question (b) If the number of companies participating in the semiconductor market increases to infinity,that is, in a perfectly competitive market, what will be the equilibrium point?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_forwardSuppose that you watch the game show over many years and find that door #1 hides the car 50% of the time, door #2 has the car 40% of the time, and door #3 has the car 10% of the time. What then is your optimal strategy? In other words, which door should you pick initially, and then should you stay or switch? What is your probability of winning with the optimal strategy? Explain.arrow_forward
- 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.arrow_forwardIn Section 5.5 we showed the following two-person, zero-sum game had a mixed strategy: Player B b1 b2 b3 a1 0 -1 2 Player A a2 5 4 -3 a3 2 3 -4 a. Which strategies are dominated? a1, a2, a3, b1, b2, b3 b. Does the game have a pure or mixed strategy?arrow_forwardWhen it comes to customs clearance of goods, customs officers and smugglers try to prevent the otherparty from predicting their respective intentions. Their respective profit metrics are as follows:■There is no general Nash equilibrium (pure strategy).■Question: What is the mixed strategy equilibrium? – find out x and yarrow_forward
- if 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_forwardA seller would like to sell a painting using second price (Vickrey) auction. The seller knows that there are three buyers and each buyer is equally likely to have High (H), Medium (M), or Low (L) valuation for the painting. The valuations of the buyers are independently distributed. Assuming that the buyers will play the Nash equilibrium in the second price auction, how much revenue will the seller make?arrow_forwardFor the following payoff table determine the value of the and optimal mixed strategy for each player using graphical procedure. Player-2 Strategy 1 2 3 Player-1 1 2 0 3 2 3 1 2arrow_forward
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