Two employees witness fraud committed in their firm. Each has two pure strategies: to become a whistleblower and report a crime, or not to report a crime. Each employee gets a payoff of 1 if the crime is reported by someone (it does not matter if both or only one employee reports). However, reporting the crime is costly. An employee who reports has to pay the cost of reporting equal to 0.5-0.25*d, where d=1 if the other employee also reports, and d=0 otherwise. Suppose that employees simultaneously decide to report or not. There is a unique mixed strategy Nash equilibrium in this game where each employee reports with the same positive probability less than 1. What is the probability that the crime is reported by at least one employee in such an equilibrium?
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- Matthew is playing snooker (more difficult variant of pool) with his friend. He is not sure which strategy to choose for his next shot. He can try and pot a relatively difficult red ball (strategy R1), which he will pot with probability 0.4. If he pots it, he will have to play the black ball, which he will pot with probability 0.3. His second option (strategy R2) is to try and pot a relatively easy red, which he will pot with probability 0.7. If he pots it, he will have to play the blue ball, which he will pot with probability 0.6. His third option, (strategy R3) is to play safe, meaning not trying to pot any ball and give a difficult shot for his opponent to then make a foul, which will give Matthew 4 points with probability 0.5. If potted, the red balls are worth 1 point each, while the blue ball is worth 5 points, and the black ball 7 points. If he does not pot any ball, he gets 0 point. By using the EMV rule, which strategy should Matthew choose? And what is his expected…[Adverse Selection] Each of the two players receives an envelope, in which there is anamount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in twoenvelopes are independent. After receiving the envelope, each individual can check exactlyhow much money is put in his/her own envelope. Then each player has the option to exchangehis/her envelope for the other individual's prize. The decisions are made simultaneously. Ifboth individuals agree to exchange, then the envelopes are exchanged; otherwise, if at leastone player chooses not to exchange, each individual keeps his/her own envelope and receivesits attached sum of money.a. Model this game as a static Bayesian game (write the normal formrepresentation) and find the Bayesian Nash equilibrium.b. Consider a new game where the probability distribution of money in eachenvelope is changed. The amount is equal to $100 with probability 90%, and is equalto each number in $0, $1, $2, ... ,$99 with probability 0.1%.…Suppose that Winnie the Pooh and Eeyore have the same value function: v(x) = x1/2 for gains and v(x) = -2(|x|)1/2 for losses. The two are also facing the same choice, between (S) $1 for sure and (G) a gamble with a 25% chance of winning $4 and a 75% chance of winning nothing. Winnie the Pooh and Eeyore both subjectively weight probabilities correctly. Winnie the Pooh codes all outcomes as gains; that is, he takes as his reference point winning nothing. For Pooh: What is the value of S? What is the value of G? Which would he choose? Eeyore codes all outcomes as losses; that is, he takes as his reference point winning $4. For Eeyore: What is the value of S? What is the value of G? Which would he choose?
- You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $1 million to $3 million. If they are wrong, their prize is decreased to $750,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is [$ blank]. Given that this is positive [blank (positive/negative)], you should [blank (should/should not)] play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is [blank]. (Hint: At what probability does playing the final round yield an expected value of zero?)Suppose 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.Consider the following variation to the Rock (R), Paper (P), Scissors (S) game:• Suppose that the Player 1 (row player) has a single type, Normal.• Player 2 (column player) has two types Normal and Simple.• A player of Normal type plays this zero-sum game as we studied in class whereas a player of type Simple always play P.• Player 2 knows whether he is Normal or Simple, but player 1does not.a) Suppose player 2 is of type Normal with probability 1/3 and of type Simple with probability (2/3). Find all pure strategy Bayesian Nash Equilibria.b) Suppose player 2 is of type Normal with probability 2/3 and of type Simple with probability (1/3). Find all pure strategy Bayesian Nash Equilibria.
- Consider the following ‘war of attrition’. Two animals are in a stand off for a prey. Theyindependently decide when to give up. Waiting is costly, but the animal giving up last winsthe prey (they each get nothing if they walk away at the exact same time). Getting the preygives a benefit of 80 while waiting costs 2 per unit of time. Formally payoffs are given asfollows:u1(t1, t2) =(−2t1 if t1 ≤ t280 − 2t2 if t1 > t2u2(t1, t2) =(80 − 2t1 if t1 < t2−2t2 if t1 ≥ t2,where ti is the amount of time animal i decided to wait. Assuming that animals aim tomaximize payoffs (consciously or not), figure out the Nash equilibria of this game by answeringthe following questions (similar to how we proceeded to solve the Bertrand game).(a) Show that there is no Nash equilibrium where both animals wait a strictly positiveamount of time. For this, consider two subcases: (i) both wait the same amount oftime, or (ii) one gives in earlier than the other.(b) Assume now that one animal, say the first one,…When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .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?
- Choice under uncertainty. Consider a coin-toss game in which the player gets $30 if they win, and $5 if they lose. The probability of winning is 50%. (a) Alan is (just) willing to pay $15 to play this game. What is Alan’s attitude to risk? Show your work.(b) Assume a market with many identical Alans, who are all forced to pay $15 to play this coin-toss game. An insurer offers an insurance policy to protect the Alans from the risk. What would be the fair (zero profit) premium on this policy? i need help with question B please.The table below shows that a sales agent can work with either low, or high amount of effort. Low effort generates$30,000, $60,000 or $100,000 profit (with probability given below), while high effort generates 60,000; 100,000 or 150, 000 (with probability given below) depending on some random factors. Bad luck (P=0.3) Medium luck (P=0.3) Good luck (P=0.4) Low effort (a=0) $30,000 $60,000 $100,000 High effort (a=1) $60,000 $100,000 $150,000 The cost of low effort is 0 and the cost of high effort is $10,000 (Formally, c=$10,000a). The net wage is wage minus cost of effort and the net profit is total profit minus wage. Suppose the firm offers the repair person a fixed wage of 13,000, what will be the net wage of the repair person and the net profit of the owner? Suppose now the owner offers the repair person the following bonus arrangement What will be the net wage of the repair person? What will be the net profit of the owner? Specify…A risk-neutral plaintiff in a lawsuit must decide whether to settle a claim or go to trial. The defendants offer $50,000 to settle now. If the plaintiff does not settle, the plaintiff believes that the probability of winning at trial is 50% if the plaintiff wins, the amount awarded to the plaintiff is X Will the plaintif settle if x is $62,500? What if X-$250,000? What is the critical value of X that would make the plaintiff indifferent between setting and going to trial? it the plaintiff were risk averse instead of risk neutral, would this critical value of X be higher or lower? If the amount to be awarded at trial with a win (X) were $62,500, then the plaintiff would settle If the amount to be awarded at trial with a win (X) were $250,000, then the plaintiff would not settle The critical value of X that would make the plaintiff indifferent between settling and going to trial is $ (Enter your response using rounded to wo decimal places)