Is every citizen revolting a Nash equilibrium of the game? Explain. Is every citizen not revolting a Nash equilibrium of the game? Explain. Are there any other Nash equilibria? If there are, specify such a Nash equilibrium, and verify that it is a Nash equilibrium. If no other Nash equilibria exit, explain why the other action profiles are not Nash equilibria.
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- Someone at a party pulls out a $100 bill and announces that he is going to auction it off. There are n=10 people at the partywho are potential bidders. The owner of the $100 bill puts forth the following procedure: All bidders simultaneously submit a written bid. Only the highest bidders pay their bid (assuming that the highest bid is positive). If m people submit the highest bid, then each receives 1/m of the $100. Each person’s strategy set is {0,1,2,...,1000}{0,1,2,...,1000} so bidding can go as high as $1,000. The payoff of a player bidding bi is:0 if bi < max{b1,b2,…,bn},and 100/m − bi if bi = max {b1,b2,…,bn}where,m is the number of bidders whose bid equals max{b1,...,bn}. How many pure-strategy Nash equilibria does this game have? 1) 0 2) 1 3) 4 4) More than 4.ЕОC 12.02 Suppose you are the mayor of a town and you want to increase safety at an intersection. A traffic light will increase safety and reduce fatality risk by 0.5% but costs $100,000. Suppose the value of human life is estimated at $10 million. Should you spend the money to install the traffic light? (Hint: to multiply 1% by 200 you follow this process: 0.01 x 200 = 2). Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Yes, since the expected benefit ($500,000) exceeds the cost. b Yes, since the expected benefit ($150,000) exceeds the cost. No, since the expected benefit ($50,000) is lower than the cost. d No, since the expected benefit ($15,000) is lower than the cost.Shimadzu, a manufacturer of precise scientific instruments, relies heavily on the efforts of its local salespeople. Selling an instrument requires either luck, high effort, or some combination of the two. A salesperson who chooses to work hard (put in high effort) has a 40 percent chance (probability of 0.4) of selling an instrument in a given year while a salesperson who chooses to slack off (put in low effort) has a 20 percent chance (probability of 0.2) of making a sale. Practically no one manages to sell more than one instrument in a single year. Contracts for salespeople are designed on a year-by-year basis. Sales staff members do not mind risk; they choose employers based only on expected wage and the disutility of effort. Disutility of effort is equivalent to $20,000 per year if they work hard and $0 if they slack off. Even if a salesperson slacks off, he or she requires a salary of at least $50,000 not to seek alternate employment. (So, the worker's net payoff in alternative…
- Wayne Enterprises had several salespersons that worked for a contract salary. To encourage them to make more sales, Wayne offered a $5,000 bonus to the salesperson who had the highest total dollar value the following month. That next month, Wendy had the highest sales. When Wendy received her next paycheck, there was no bonus. If Wendy sues Wayne to recover the $5,000 bonus, the likely result will be A. Wendy will lose because she already had a contract so there was no consideration B. Wendy will win because the offer of a bonus for high sales constituted consideration because it entailed additional performance by both parties C. Wendy will lose unless the promise was in writing. D. Wendy will win because of moral considerationCountry A is rich and country B is poor. Consequently, residents of country B want to immigrate to country A. The trouble is that there is no legal way to do. So they attempt to cross the border Illegally. There are 3 border crossings at which a resident of B may attempt to cross the border. An attempt is successful if there is no border guard at the crossing, and unsuccessful if there is a guard at the crossing. Country A has only 1 border guard. Model the game in which a resident of country B attempts to enter country A at one of the 3 border crossings, and the government of country A chooses to post its border guard at one of the 3 border crossings. In this game, each player has 3 pure strategies. A) What are the ultimate outcomes in this game? B) What are the player's Bernoulli Payoffs? C) Find a mixed strategy equilibrium of the game.There is a city, which looks like a trapezoid, as shown below. Citizens liveuniformly distributed all over the city. Two ice-cream vendors, A and B, must independently set up stores in the city. Each citizen buys from the vendor closest to their location and when equidistant from both vendors they choose bycoin toss. Each vendor’s aim is to maximize the expected number of customers. A choice oflocation by the two vendors is a Nash equilibrium if no vendor can do better by deviatingunilaterally. Does this game have a Nash equilibrium? If so, describe it. If not, explain why not.
- First Player can invest $1.00 with Second Player (low reliance) or $2.00 (high reliance). Based on the payoffs shown below, what is the probability of performance that makes High Reliance optimal? Write your answer as a two digit integer. E.g., if the answer is 33%, write 33. Second Player Perform Breach Invest & Low Reliance 0.25 1.0 First Player 0.25 -1.0 Invest & High Reliance 0.5 1.0 0.75 -2.0Bill owes Bob $36. Just before Bill pays him the money, he gives Bob the opportunity to play a dice game to potentially win more money. The rules of this game are as follows: If Bob rolls doubles (probability 1/6), Bill will Bob double ($72). If he misses doubles on pay the first try, he can try again or settle for half the money ($18). If he makes doubles on the second try Bill will again pay-up double ($72), but if Bob misses doubles on the second try Bill will only pay him one-third ($12). Should Bob decide to play the dice game with Bill, or insist that he pay the $36 now? Use a decision tree to support your answer.Suppose that a car - rental agency offers insurance for a week that costs $125. A minor fender bender will cost 34000 whereas a major accident might cost $16 comma 000 in repairs. Without the insurance, you would be personally liable for any damages. There are two decision alternatives: take the insurance, or do not take the insurance. You researched insurance industry statistics and found out that the probability of a major accident is 0.04% and that the probability of a fender bender is 0.18%. The expected payoff if you buy the insurance is $125.00. The expected payoff if you do not buy the insurance is $12.52. Develop a utility function for the payoffs associated with this decision for a risk-averse person. Determine the decision that would result using the utilities instead of the payoffs. Based on the expected payoffs, the best decision is to not purchase the insurance. Are these two decisions consistent?
- In a series of houses actually invaded by smallpox, 70% of the inhabitants are attacked and 85% have been vaccinated. What is the lowest percentage of the vaccinated that must have been attacked?1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.