A master student interested in pursuing a PhD is deciding between two courses: advanced game theory x = A and introduction to game theory x = I. The student can be one of two types: 0= L or 0= H. The PhD admission officer can observe the courses chosen by the student x = {A, I} but not the type of the student 0. Before observing the course chosen by the student, she believes both types are equally likely. She admits students only if she is sure that they are type 0 = H (that is if she believes P(0 = H|x) = 1). The student gets 10 units of utility from being admitted to a PhD and 0 units if not admitted, and pays costs c(0) if she chooses advanced game theory and costs 0 if she chooses introduction to game theory. We assume that c(H) = 0 < c(L) = 15. 1) How do we call a situation of asymmetric information in which the informed player moves first? What if the uninformed player moves first?
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- Two identically able agents are competing for a promotion. The promotion is awarded on the basis of output (whomever has the highest output, gets the promotion). Because there are only two workers competing for one prize, the losing prize=0 and the winning prize =P. The output for each agent is equal to his or her effort level times a productivity parameter (d). (i.e. Q2=dE1 , Q2=dE2). If the distribution of “relative luck” is uniform, the probability of winning the promotion for agent 1 will be a function of his effort (E1) and the effort level of Agent 2 (E2). The formula is given by...Prob(win)=0.5 + α(E1-E2), where α is a parameter that reflects uncertainty and errors in measurement. High measurement errors are associated with small values of α (think about this: if there are high measurement errors, then the level of an agent’s effort will have a smaller effect on his/her chances of winning). Using this information, please answer the following questions. Both workers have a…Given the both answer..Consider the Hawk–Dove situation shown here. a. Show that an ESS uses hawk with probability 2/3.b. In this chapter, we’ve only allowed a mutation to be of a single strategy.Departing from that assumption, consider a small mutation in whichhalf of the mutants are hawks and half are doves (i.e., they use onlypure strategies). Determine whether the ESS in part (a) is immune tothis mutation; that is, determine whether the ESS has higher fitnessthan that of each of these mutants.
- A few minutes ago, Joe Doe learned that his company was having a bad year and thus merit salary increases will be smaller than expected. His division’s budget has been set and so he knows that he will receive a salary increase of $400 over his present salary. Joe Doe has also been offered a transfer to another division in the company. He is unsure of the salary situation in the other division. However, his best information leads him to conclude that if he took the new job, there is a 60% chance that he would receive a salary increase of $600 over his present salary, and a 40% chance that he would receive only a $150 increase over his present salary. To summarize, Joe Doe can either stick with his current job and get a salary increase of $400, or take a transfer to a new job and get a salary increase of either $600 with a 60% probability, or $150 with a 40% probability. Amount ($X) Value (v($X)) $0 -5 $150 -2.5 $200 -2 $300 0 $350 0.5 $400 1 $600 1.85…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?JUST ANSWER SUBPART 2 There are two individuals, Individual A and Individual B. Individual A has an income (Y) of 500 million Rupiah per year. If Individual A is sick, he will lose 25% of his income. Meanwhile, Individual B has an income (Y) of 100 million Rupiah per year, and if Individual B is sick, he will lose 75% of his income. The probability of Individual A and Individual B being sick is the same, which is 10%. If the satisfaction level of Individual A and Individual B is determined by their income level, based on the following function U(Y)=ln Y, would Individual A and Individual B prefer not to have health insurance? Explain Faced with fair actuarially insurance, how much premium is offered to Individual A? Is the premium rate offered the same for Individual B? Explain with the support of graphic illustrations. The government decides to provide compulsory health insurance with a premium rate for Individual A and Individual B, which is 2% of the income of each individual. In…
- An experiment can result in any of the outcomes 1, 2, or 3.(a) If there are two different wagers, withr1(1) = 1, r1(2) = 8, r1(3) = −10r2(1) = 2, r2(2) = 12, r2(3) = −16.Is an arbitrage possible? Do not just answer a yes or no. Show your working.For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the table. Black Silver White Korea 33 34 35 Japan 23 9 24 America 16 25 34 Germany 19 16 32 One car is selected at random from this group. Find the probability that the selected car is a black or white car manufactured in Korea. not manufactured in Japan. is a white car, given that it was manufactured in America. Are the events ‘Korea’ and ‘Black’ Mutually Exclusive? Justify your response. Are the events ‘Korea’ and ‘Black’ Independent? Justify your responseIn the game of blackjack as played in casinos in Las Vegas, Atlantic City, and Niagara Falls, as well as in many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a hand is about 45%. Find the probability that an average player wins. a.Twice in 5 hands. b. Ten or more times in 25 hands. Arrivals 0 1 2 3 4 5 6 7 8 Frequency 14 31 47 41 29 21 10 5 2
- Suppose that there are two types of entrepreneur: skilled and unskilled. Skilled entrepreneurs have a probability p = 2/3 of success if they get the loan. Unskilled entrepreneurs have zero chance of being successful. Despite that, assume that unskilled entrepreneurs want to take up the loan, because it is cool to say you have a startup. The bank does not observe skill. The share of skilled entrepreneurs is s. Question 1: 1A). TRUE OR FALSE: If L = 2, R = 6, and s = 0.5, then the bank would have zero expected profits, but entrepreneurs would never take up the loan. 1B. ) TRUE OR FALSE: If the loan amount is L = 2, the payback amount is R = 3, and the share of skilled entrepreneurs is s = 0.9, then the bank will have positive expected profits.Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!5 Historical data indicates that only 35% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 12 cable customers, what is the probability that between 3 and 5 (inclusive) customers are willing to switch companies? (Use TI 84 and round answer to at least 3 decimal places)