Question 4: Centipede gameThe centipede game, first introduced by Robert Rosenthal in 1981, is an extensive form game inwhich two players take turns choosing either to take a slightly larger share of an increasing pot,or to pass the pot to the other player. In other words, player 1 chooses between D (Down) and A(Across), where D is pocketing the pot and A is passing the pot to the player 2. Similarly, player 2chooses between A and D.The payoffs are arranged so that if one passes the pot to one's opponent and the opponent takesthe pot on the next round, one receives slightly less than if one had taken the pot on this round.D1(1,0)A 2 A 1 A 2 A 1 ADD(0,2)(3,1)DD(2,4) (4,3)- (3,5)1. Find the subgame perfect Nash Equilibrium using backward induction.

from the given data, we can see player 1 plays 3 times and player 2 plays 2 times. to arrive at…

Answered: or to pass the pot to the other player.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel. -if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000 let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23 u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053 FILL IN THE BLANK if you play 2500 times, and Let, x (x bar)= the mean winnings (or…
A chef is trying out a new recipe he has been working on and wants to see if it will sell better than his old one. To find out, he performs an experiment where he randomly assigns 20 people to try his new recipe and 20 people to try his old one. He asks each group how much they would be willing to pay for their food, and he finds that the group with the old recipe would pay an average of $20.00 and the second would pay an average of $26.00. He then performs an independent samples t-test between these groups. a. Suppose the sample variance for the price of the chef’s old recipe is $2.00, and the sample variance for the new recipe is $3.00. Perform a one-tailed t-test at a significance level of α = 0.01 and explain what the result means (how does the new recipe compare to the old one?). b. To evaluate the magnitude of effect size, compute the estimated Cohen’s d. Briefly describe what it means, and comment on the strength of the effect: is it weak, moderate or strong?
A roulette wheel has 30 slots, consisting of 2 blues, 8 whites, and 20 red slots. You will receive P100 if the roulette stops spinning on a blue slot, you will receive P50 on a white slot, but you will be penalized P10 if the roulette stops spinning on a red slot. Let X be the amount you will recieve (or pay). The probaility of receiving P50 is 2/30 or 1/15, and of receiving P50 is 8/30 or 4/15. What is the probability of penalty of P10? 2/3 1/3 -2/3
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Two students in a microeconomics class traveled to a football game just before the midterm and drank too much to be able to study. So they telephoned their professor and lied to him, saying that a flat tire had delayed them. "No problem," said the professor. "Take the test tomorrow." When they arrived, the professor put each student in a separate room for taking the test. The first question, worth 5 points, was easy. The second question was worth 95 points: "Which tire?" Calculate, for each student, the expected test score.
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An investor wants to exactly replicate the put option's payoff so he considers to buy X shares of the stock and Y shares of bonds. Suppose the stock price is $70 and the bond price with coupon rate 5% is $100. The stock price will either go up 15% or down 8% in one year. There are one European call option and one European put option with exercise price of $70 that will be expired in one year. Short selling is allowed. What are the values of X and Y?
Three workers at a domino's pack the take out pizza orders.ramu packs 40 of the orders but fails to include a chilli flakes sachet 4 %of the time. Raju packs 30 %of the orders but omits the chilli flakes sachet 2 %of the time. Sam packs 30 %of the orders but fails to include chilli flakes sachet 3% of the time. You received the pizza delivery and there was no chilli flakes sachets. What is the probability that Sam made the packing for the order
The player pays a fee of $5 to play. The player then rolls a 12-sided die three times. If the player rolls a 7 on any of the three rolls, they win a prize. The prize is determined by the number of 7s rolled. If the player rolls one 7, they win $5. If the player rolls two 7s, they win a $10. If the player rolls three 7s, they win $20. Compare the theoretical results of the game to the experimental results, including a discussion of whether the results were typical or rare. Theoretical results: Roll (including all 3 rolls) Result Money earned 1 7,7,7 $15 2 2,4,5 $5 3 5,7,9 $5 4 1,9,3 $0 5 2,12,7 $5 6 3,12,3 $0 7 7,4,8 $5 8 6,7,7 $10 9 5,12,4 $0 10 7,5,7 $10 Experimental results: Roll (including all 3 rolls) Result Money earned 1 1,3,7 $5 2 3,6,4 $0 3 7,6,9 $5 4 8,7,7 $10 5 11,4,1 $0 6 6,5,7 $7 7 4,6,3 $0 8 7,1,9 $7 9…
Use the last diminisher method to solve the following problem. 1. A piece of property valued at $50,000 is divided among five players (P1, P2, P3, P4, P5) using the last diminisher method. The players play in a fixed order, with P1 first, P2 second, and so on. In round 1, P1 makes the first cut and makes a claim on a C-piece of the land. For each of the remaining players, the value of the current C-piece at the time it is their turn is given in the following table: Player 2 Player 3 Player 4 Player 5 Value of $12,000 $13,000 $9,000 $8,000 current C-piece a.) What is the fair share for each player? Show your work in the space provided below. b.) What does player 2 do with the piece and why? c.) What does player 3 do with the piece and why? d.) What does player 4 do with the piece and why? e.) What does player 5 do with the piece and why? f.) Who gets the piece at the end of round 1 and why is it that person? g.) What is the value of the piece?

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