A person has been mugged in the street by a thief, and there are n witnesses. All of the witnesses prefer someone else to chase the thief but none of them want to be the person trying to catch her. Each person gets 0 utility if the crime goes unreported, v if the crime is reported by someone else, and v −c if they report the crime. Moreover, we assume that the cost of chasing the thief is less than the utility of catching the thief: c < v. a. Define the strategic game described above. b. Find players’ best responses. c. Find the Nash equilibria of the game.
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Problem 4
A person has been mugged in the street by a thief, and there are n witnesses. All of the
witnesses prefer someone else to chase the thief but none of them want to be the person
trying to catch her. Each person gets 0 utility if the crime goes unreported, v if the crime is
reported by someone else, and v −c if they report the crime. Moreover, we assume that the
cost of chasing the thief is less than the utility of catching the thief: c < v.
a. Define the strategic game described above.
b. Find players’ best responses.
c. Find the Nash equilibria of the game.
Step by step
Solved in 2 steps
- how then can we find the total utility given q1=24, q2=30 and q3=15Suppose that a decision maker faced with four decisions alternatives and four state of nature developing the following profit payoff table: Outcomes Alternatives S1 S2 S3 S4 A1 14 9 10 5 A2 11 10 8 7 A3 9 10 10 11 A4 8 10 11 13 Use Maximax, Maximin, Criterion of realism (? = 0.55, and ? = 0.4), Laplace, and Minimax regret to find the best alternative.Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen, she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function U(x)=(x)^0.5 Suppose that she has the option to buy traveler’s checks. If her backpack is stolen and she is carrying traveler’s checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler’s check. In other words, the price of a $1 traveler’s check is $(1+p). If the purchase of traveler’s checks is a fair bet, then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet, then the price (1+p) = $1.25.
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- Utility functions incorporate a decision maker’s attitude towards risk. Let’s assume that the following utilities were assessed for Danica Wary. x u(x) -$2,000 0 -$500 62 $0 75 $400 80 $5,000 100 Would a risk neutral decision maker be willing to take the following deal: 30% chance of winning $5,000, 40% chance of winning $400 and a 30% chance of losing $2,000? Using the utilities given in the table above, determine whether Danica would be willing to take the deal described in part a? Is Danica risk averse or is she a risk taker? What is her risk premium for this deal?A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and if it does not. Assume that the Bernoulli utility function takes the form u(x) = with r > 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA? Alex plays football for a local club in Kumasi. If he does not suffer any injury by the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coach worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = Assume he could buy insurance at price P that could pay $9,900 in case of injury. What is the highest value of P that makes it worthwhile for Alex to purchase insurance? What is the certainty…By using the expected utility theory approach with u(x)=x2, choose the optimal decision for three different possible outcomes with probabilities p(ω1)=1/2, p(ω2)=p(ω3)=1/4, rewards R(d1,ω1)=£49,R(d1,ω2)=R(d1,ω3)=£25, R(d2,ω1)=£36,R(d2,ω2)=£100,R(d2,ω3)=£0, R(d3,ω1)=£81,R(d3,ω2)=R(d3,ω3)=£0