Rita is playing a game of chance in which she tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random. This game is this: Rita tosses the dart once. She wins $1 if the dart lands in slice 1. $2 if the dart lands in slice 2, $5 if the dart lands in slice 3, and $8 if the dart lands in slice 4. She loses $3 if the dart lands in slices 5, 6, 7, or 8. (If necessary, consult a list of formulas,.) (a) Find the expected value of playing the game. | dollars (b) What can Rita expect in the long run, after playing the game many times? Rita can expect to gain money. She can expect to win | dollars per toss. O Rita can expect to lose money. She can expect to lose dollars per toss. O Rita can expect to break even (neither gain nor lose money).

Rita is playing a game of chance in which she tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random. This game is this: Rita tosses the dart once. She wins $1 if the dart lands in slice 1. $2 if the dart lands in slice 2, $5 if the dart lands in slice 3, and $8 if the dart lands in slice 4. She loses $3 if the dart lands in slices 5, 6, 7, or 8. (If necessary, consult a list of formulas,.) (a) Find the expected value of playing the game. | dollars (b) What can Rita expect in the long run, after playing the game many times? Rita can expect to gain money. She can expect to win | dollars per toss. O Rita can expect to lose money. She can expect to lose dollars per toss. O Rita can expect to break even (neither gain nor lose money).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. Suppose we play the following game. I give you $100 for your initial bankroll. At each time n, you decide how much of your current wealth to bet. You cannot borrow money. You can only play with the money I gave you in the beginning or any money that you have won so far. The game is simple. At each time n ≥ 1, you decide the amount to bet. I will roll a fair die. If the die comes up 1,2,3,..., or 5, you win; if the die comes up 6, then you lose. IOW, if you bet $10 on the first roll, you will either have $90 or $110 after the first roll. (a) Suppose you wish to maximize your profit on the first roll. How much should you bet? (Most of you will get this wrong.) (b) What is the expected profit on the first roll if your bet is b with 0 ≤ b ≤ 100? (c) Suppose you wish to maximize your expected profit on the first roll. How much should you bet? (d) Suppose you wish to maximize your expected profit betting on the nth roll. How much of your current wealth do you bet? (e) Let X₂, be your…
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Consider a situation of after-match penalty shoot-out. The striker can target either East or West side of the goal. If he targets West, with 80% chance he shoots on target. If he shoots East, he is accurate with 75%. The goalkeeper has to choose the corner to jump to. If he does not guess the corner correctly and the shot is on target, then the striker scores. If the striker shoots West, the shot is on target and the goalkeeperjumps West, then with 75% chance he saves the goal. If the striker shoots East, the shot is on target and the goalkeeper jumps East, then with chance of 2/3 he saves the goal. Suppose, that it is a zero-sum game and if the striker scores his payoﬀ is 1, otherwise it is 0.1. Formulate this situation as a strategic game and Find all Nash equilibria of the game.
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