Question 6 You are making a bid to take over a company that George currently owns and controls. George has private information about whether the company is "good" or "bad," but you only know that the company is bad with probability and good with probability 2. You are well aware that he has this private information. As you can see from the matrix below, your expertise lies in controlling "good" companies. If the company is "bad," then it is more valuable under George's control than yours. Value under George's Control Value under Your Control $40
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- 3. Han Solo is delivering illicit cargo to the rebel forces on Alderaan, a planet blockaded by the galactic empire. In order to deliver his cargo successfully, Han Solo must pass 2 checkpoints, each of which will not detect his cargo with probability q. If Han Solos cargo is detected at one or more checkpoints, then his final wealth is 0. If Han Solo passes both checkpoints undetected, then his final wealth is 100. Han Solo's risk- preference is described by Bernoulli utility function Vw. Thus Han Solo's wealth is described by a lottery: 100 with probability q?, 0 with probability 1- q. (a) What is Han Solo's expected utility? Suppose an Imperial officer makes an offer to Han Solo. The officer will reduce number of checkpoints from 2 to 1, but if Han Solo gets through, he has to pay k to the officer. If Han Solo gets caught, his payoff is 0. If he agrees to this arrangement, then his final wealth is described by a lottery: 100 – k with probability q, 0 with probability 1- q. (b) What…2. Kier, in The scenario, wants to determine how each of the 3 companies will decide on possible new investments. He was able to determine the new investment pay off for each of the three choices as well as the probability of the two types of market. If a company will launch product 1, it will gain 50,000 if the market is successful and lose 50,000 if the market is a failure. If a company will launch product 2, it will gain 25,000 if the market is successful and lose 25,000 if the market will fail. If a company decides not to launch any of the product, it will not be affected whether the market will succeed or fail. There is a 56% probability that the market will succeed and 44% probability that the market will fail. What will be the companies decision based on EMV? What is the decision of each company based on expected utility value?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…
- 17. Suppose a risk-neutral power plant needs 10,000 tons of coal for its operations next month. It is uncertain about the future price of coal. Today it sells for $60 a ton but next month it could be $50 or $70 (with equal probability). How much would the power plant be willing to pay today for an option to buy a ton of coal next month at today's price? (Ignore discounting over the short period of a month.) а. 5 b. 4 с. 3 d. NOTE: I KNOW THAT THE ANSWER IS (A), BUT PLEASE INCLUDE ALL THE STEPS HOW TO SOLVE THE PROBLEM BECAUSE I NEED TO PRACTICE. THANK YOU.1Y You have to decide whether to invest $100 in a friend's enterprise, where in a year's time the money will increase to $150. You have agreed that your friend will split the profits evenly each year with you. Your alternative is to keep at the bank at an interest rate of r. Suppose this game is played repeatedly infinitely often. The rate of interest between any two successive periods is r, the same as that in the bank and the same for you and your friend. What is the cut-off interest rate which will make cooperation possible?3:51 9 M 23 The mixed strategy Nash equilibrium of the following * game is Player 2 R. L Player 1 U 2,2 3,1 D 3.-1 0.0 U with 3/4 probability and D with 1/4 probability for player 1; L with1/2 probability and probability for player 2 with 1/2 U with 1/2 probability and D with 1/2 probability for player 1; L with1/4 probability and R with 3/4 probability for player 2 U with 1/4 probability and D with 3/4 probability for player 1; L with1/2 probability and R with 1/2 probability for player 2 O None of the above. U with 1/2 probability and D with 1/2 probability for player 1; L with3/4 probability and R with 1/4 probability for player 2
- Text of the problem from 'An introduction to decision theory' by Martin Peterson: You prefer a fifty-fifty chance of winning either $100 or $10 to a lottery in which you win $200 with a probability of 1/4, $50 with a probability of 1/4, and $10 with a probability of 1/2. You also prefer a fifty-fifty chance of winning either $200 or $50 to receiving $100 for sure. Are your preferences consistent with von Neumann and Morgenstern’s axioms? The book proposes as solution 'No. Your preferences violate the independence axiom.' without proposing the steps to reach that solution and I don't know why it is correct.9. Find all of the Nash equilibria for the three-player game here. Player 1 a b Player 3: A Player 2 X y Z 1,1,0 2,0,0 2,0,0 3,2,1 1,2,3 0,1,2 2,0,0 0,2,3 3,1,1 Player 1 a b C Player 1 Player 3: C X Player 2 y 2,0,0 0,1,2 0,1,1 1,2,1 3,1,2 0,1,2 a b C Player 3: B Player 2 X 2,0,0 1,2,0 0,1,2 Z 0,1,2 0,1,2 1,1,2 y 0,0,1 1,2,1 2,2,1 Z 2,1,2 1,2,1 2,1,02. Consider the following Bayesian game with two players. Both players move simultaneously and player 1 can choose either H or L, while player 2's options are G, M, and D. With probability 1/2 the payoffs are given by "Game 1" : GMD H 1,2 1,0 1,3 L 2,4 0,0 0,5 and with probability 1/2 the payoffs are according to "Game 2" : G |M|D H 1,2 1,3 1,0 L 2,4 0,5 0,0 (a) Find the Nash Equilibria when neither player knows which game is actually played. (b) Assume now that player 2 knows which one among the two games is actually being played. Check that the game has a unique Bayesian Nash Equilibrium.
- You are one of five risk-neutral bidders participating in an independent private values auction. Each bidder perceives that bidders' valuations for the item are evenly distributed between $20,000 and $50,000. For each of the following auction t determine your optimal bidding strategy if you value the item at $35,000. a. First-price, sealed-bid auction. O Bid $20,00. O Bid $50,00. O Bid $35,00. O Bid $32,000 b. Dutch auction O Let the auctioneer continue to lower the price until it reaches $20,000, and then yell "Minel". O Let the auctioneer continue to lower the price until it reaches $35.000, and then yell "Mine!" O Let the auctioneer continue to lower the price until it reaches $32,000, and then yell "Mine!" O Let the auctioneer continue to lower the price until it reaches $50,000, and then yell "Mine!". C. ond-price, sealed-bid auction O Bid $50,00. O Bid $35.000 O Bid $32,00. b. Dutch auction. O Let the auctioneer continue to lower the price until it reaches $20,000, and then yell…A6. 1.Adam and Zoey are competing fish and chips sellers in Linear City. They are located at the twoopposing ends of the town’s 3-mile-long Main Street. The 1700 inhabitants of the town are distributeduniformly on Main Street and each of them eats at most one portion of fish and chips for lunch. People’sdisutility from getting to a fish and chips stand and back home amounts to $2 for each mile of distanceto the stand. The marginal cost of producing one portion of fish and chips is $9. The consumers areuniformly distributed along the street. Each consumer has a valuation of $29.0 for the product. Supposethat both Zoey and Adam can advertise at zero cost to inform everyone about their business. Find theequilibrium price of Zoey if neither of the two sellers advertises.3. Suppose that Jon Snow's utility function is given by U(I)=501 where I represents annual income in thousands of dollars. a. Is Jon risk loving, risk neutral, or risk averse? Explain b. Suppose that Jon is currently earning an income of $1000 and can earn that income next year with certainty. He is offered a chance to take a new night watch job that offers a 0.25 probability of earning $2000 and a 0.75 probability of earning $500. Should he take the new night watch job?